X010 Trigonometry Find Angle From 3 Sides

Approved & Edited by ProProfs Editorial Team

At ProProfs Quizzes, our dedicated in-house team of experts takes pride in their work. With a sharp eye for detail, they meticulously review each quiz. This ensures that every quiz, taken by over 100 million users, meets our standards of accuracy, clarity, and engagement.

Learn about Our Editorial Process

| Written by Anthony Nunan

Anthony Nunan

Community Contributor

Quizzes Created: 159 | Total Attempts: 45,981

Questions: 30 | Attempts: 48 | Updated: Apr 21, 2023

Questions

Settings

Feedback

During the Quiz End of Quiz

Play as

Quiz Flashcard

Create your own Quiz

X010 Trigonometry Find Angle From 3 Sides - Quiz

When asked for a fraction, do not simplify ie if the answer is 2/4 do not simplify to 1/2

Questions and Answers

1.

$The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a tan ratio, what fraction will be created for the inverse tan calculation? - ProProfs$

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a tan ratio, what fraction will be created for the inverse tan calculation?

Explanation
When finding the inverse, we create a fraction from the two sides. Sin = 0pp/Hyp, Cos = Adj/Hyp, and Tan = Opp/Adj. We remember this using SOH CAH TOA.

Rate this question:

4
2.

$The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a tan ratio, what fraction will be created for the inverse tan calculation? - ProProfs$

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a tan ratio, what fraction will be created for the inverse tan calculation?

Explanation
When finding the inverse, we create a fraction from the two sides. Sin = 0pp/Hyp, Cos = Adj/Hyp, and Tan = Opp/Adj. We remember this using SOH CAH TOA.

Rate this question:

4
3.

$The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a tan ratio, what fraction will be created for the inverse tan calculation? - ProProfs$

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a tan ratio, what fraction will be created for the inverse tan calculation?

Explanation
When finding the inverse, we create a fraction from the two sides. Sin = 0pp/Hyp, Cos = Adj/Hyp, and Tan = Opp/Adj. We remember this using SOH CAH TOA.

Rate this question:

4
4.

$The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a tan ratio, what fraction will be created for the inverse tan calculation? - ProProfs$

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a tan ratio, what fraction will be created for the inverse tan calculation?

Explanation
When finding the inverse, we create a fraction from the two sides. Sin = 0pp/Hyp, Cos = Adj/Hyp, and Tan = Opp/Adj. We remember this using SOH CAH TOA.

Rate this question:

4
5.

$The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a tan ratio, what fraction will be created for the inverse tan calculation? - ProProfs$

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a tan ratio, what fraction will be created for the inverse tan calculation?

Explanation
When finding the inverse, we create a fraction from the two sides. Sin = 0pp/Hyp, Cos = Adj/Hyp, and Tan = Opp/Adj. We remember this using SOH CAH TOA.

Rate this question:

4
6.

$The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a cos ratio, what fraction will be created for the inverse cos calculation? - ProProfs$

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a cos ratio, what fraction will be created for the inverse cos calculation?

Explanation
When finding the inverse, we create a fraction from the two sides. Sin = 0pp/Hyp, Cos = Adj/Hyp, and Tan = Opp/Adj. We remember this using SOH CAH TOA.

Rate this question:

4
7.

$The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a cos ratio, what fraction will be created for the inverse cos calculation? - ProProfs$

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a cos ratio, what fraction will be created for the inverse cos calculation?

Explanation
When finding the inverse, we create a fraction from the two sides. Sin = 0pp/Hyp, Cos = Adj/Hyp, and Tan = Opp/Adj. We remember this using SOH CAH TOA.

Rate this question:

4
8.

$The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a cos ratio, what fraction will be created for the inverse cos calculation? - ProProfs$

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a cos ratio, what fraction will be created for the inverse cos calculation?

Explanation
When finding the inverse, we create a fraction from the two sides. Sin = 0pp/Hyp, Cos = Adj/Hyp, and Tan = Opp/Adj. We remember this using SOH CAH TOA.

Rate this question:

4
9.

$The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a cos ratio, what fraction will be created for the inverse cos calculation? - ProProfs$

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a cos ratio, what fraction will be created for the inverse cos calculation?

Explanation
When finding the inverse, we create a fraction from the two sides. Sin = 0pp/Hyp, Cos = Adj/Hyp, and Tan = Opp/Adj. We remember this using SOH CAH TOA.

Rate this question:

4
10.

$The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a cos ratio, what fraction will be created for the inverse cos calculation? - ProProfs$

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a cos ratio, what fraction will be created for the inverse cos calculation?

Explanation
When finding the inverse, we create a fraction from the two sides. Sin = 0pp/Hyp, Cos = Adj/Hyp, and Tan = Opp/Adj. We remember this using SOH CAH TOA.

Rate this question:

4
11.

$The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a sin ratio, what fraction will be created for the inverse sin calculation? - ProProfs$

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a sin ratio, what fraction will be created for the inverse sin calculation?

Explanation
When finding the inverse, we create a fraction from the two sides. Sin = 0pp/Hyp, Cos = Adj/Hyp, and Tan = Opp/Adj. We remember this using SOH CAH TOA.

Rate this question:

4
12.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

Explanation
You can use any ratio, but you must use the inverse function to find a missing angle.
My preference is to use COS because it is easiest to detect the apex of the angle, and nominate the adjacent and hypotenuse. Less room for error.

Rate this question:

4
13.

$The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a sin ratio, what fraction will be created for the inverse sin calculation? - ProProfs$

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a sin ratio, what fraction will be created for the inverse sin calculation?

Explanation
When finding the inverse, we create a fraction from the two sides. Sin = 0pp/Hyp, Cos = Adj/Hyp, and Tan = Opp/Adj. We remember this using SOH CAH TOA.

Rate this question:

4
14.

$The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a sin ratio, what fraction will be created for the inverse sin calculation? - ProProfs$

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a sin ratio, what fraction will be created for the inverse sin calculation?

Explanation
When finding the inverse, we create a fraction from the two sides. Sin = 0pp/Hyp, Cos = Adj/Hyp, and Tan = Opp/Adj. We remember this using SOH CAH TOA.

Rate this question:

4
15.

$The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a sin ratio, what fraction will be created for the inverse sin calculation? - ProProfs$

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a sin ratio, what fraction will be created for the inverse sin calculation?

Explanation
When finding the inverse, we create a fraction from the two sides. Sin = 0pp/Hyp, Cos = Adj/Hyp, and Tan = Opp/Adj. We remember this using SOH CAH TOA.

Rate this question:

4
16.

$The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a sin ratio, what fraction will be created for the inverse sin calculation? - ProProfs$

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a sin ratio, what fraction will be created for the inverse sin calculation?

Explanation
When finding the inverse, we create a fraction from the two sides. Sin = 0pp/Hyp, Cos = Adj/Hyp, and Tan = Opp/Adj. We remember this using SOH CAH TOA.

Rate this question:

4
17.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

Explanation
You can use any ratio, but you must use the inverse function to find a missing angle.
My preference is to use COS because it is easiest to detect the apex of the angle, and nominate the adjacent and hypotenuse. Less room for error.

Rate this question:

4
18.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

Explanation
You can use any ratio, but you must use the inverse function to find a missing angle.
My preference is to use COS because it is easiest to detect the apex of the angle, and nominate the adjacent and hypotenuse. Less room for error.

Rate this question:

4
19.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

Explanation
You can use any ratio, but you must use the inverse function to find a missing angle.
My preference is to use COS because it is easiest to detect the apex of the angle, and nominate the adjacent and hypotenuse. Less room for error.

Rate this question:

4
20.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

Explanation
You can use any ratio, but you must use the inverse function to find a missing angle.
My preference is to use COS because it is easiest to detect the apex of the angle, and nominate the adjacent and hypotenuse. Less room for error.

Rate this question:

4
21.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

Explanation
You can use any ratio, but you must use the inverse function to find a missing angle.
My preference is to use COS because it is easiest to detect the apex of the angle, and nominate the adjacent and hypotenuse. Less room for error.

Rate this question:

4
22.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

Explanation
You can use any ratio, but you must use the inverse function to find a missing angle.
My preference is to use COS because it is easiest to detect the apex of the angle, and nominate the adjacent and hypotenuse. Less room for error.

Rate this question:

4
23.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

Explanation
You can use any ratio, but you must use the inverse function to find a missing angle.
My preference is to use COS because it is easiest to detect the apex of the angle, and nominate the adjacent and hypotenuse. Less room for error.

Rate this question:

4
24.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

Explanation
You can use any ratio, but you must use the inverse function to find a missing angle.
My preference is to use COS because it is easiest to detect the apex of the angle, and nominate the adjacent and hypotenuse. Less room for error.

Rate this question:

4
25.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

Explanation
You can use any ratio, but you must use the inverse function to find a missing angle.
My preference is to use COS because it is easiest to detect the apex of the angle, and nominate the adjacent and hypotenuse. Less room for error.

Rate this question:

4
26.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

Explanation
You can use any ratio, but you must use the inverse function to find a missing angle.
My preference is to use COS because it is easiest to detect the apex of the angle, and nominate the adjacent and hypotenuse. Less room for error.

Rate this question:

4
27.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

Explanation
You can use any ratio, but you must use the inverse function to find a missing angle.
My preference is to use COS because it is easiest to detect the apex of the angle, and nominate the adjacent and hypotenuse. Less room for error.

Rate this question:

4
28.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

Explanation
You can use any ratio, but you must use the inverse function to find a missing angle.
My preference is to use COS because it is easiest to detect the apex of the angle, and nominate the adjacent and hypotenuse. Less room for error.

Rate this question:

4
29.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

Explanation
You can use any ratio, but you must use the inverse function to find a missing angle.
My preference is to use COS because it is easiest to detect the apex of the angle, and nominate the adjacent and hypotenuse. Less room for error.

Rate this question:

4
30.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

Explanation
You can use any ratio, but you must use the inverse function to find a missing angle.
My preference is to use COS because it is easiest to detect the apex of the angle, and nominate the adjacent and hypotenuse. Less room for error.

Rate this question:

4

X010 Trigonometry Find Angle From 3 Sides

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a tan ratio, what fraction will be created for the inverse tan calculation?

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a tan ratio, what fraction will be created for the inverse tan calculation?

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a tan ratio, what fraction will be created for the inverse tan calculation?

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a tan ratio, what fraction will be created for the inverse tan calculation?

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a tan ratio, what fraction will be created for the inverse tan calculation?

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a cos ratio, what fraction will be created for the inverse cos calculation?

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a cos ratio, what fraction will be created for the inverse cos calculation?

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a cos ratio, what fraction will be created for the inverse cos calculation?

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a cos ratio, what fraction will be created for the inverse cos calculation?

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a cos ratio, what fraction will be created for the inverse cos calculation?

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a sin ratio, what fraction will be created for the inverse sin calculation?

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a sin ratio, what fraction will be created for the inverse sin calculation?

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a sin ratio, what fraction will be created for the inverse sin calculation?

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a sin ratio, what fraction will be created for the inverse sin calculation?

The triangle below gives the lengths of all three sides, and asks to find the angle. If this problem is to be solved using a sin ratio, what fraction will be created for the inverse sin calculation?

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.

The triangle below gives the lengths of all three sides, and asks to find the angle. Using any ratio, calculate the value of the missing angle to the nearest degree. Given your answer as a whole number only.