X010 Trigonometry Find Angle From 3 Sides

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| By Anthony Nunan
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Anthony Nunan
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Quizzes Created: 132 | Total Attempts: 48,392
| Attempts: 69 | Questions: 30 | Updated: Apr 21, 2025
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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? 

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.

Submit
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About This 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

2)

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You may optionally provide this to label your report, leaderboard, or certificate.

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 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.

Submit

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 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.

Submit

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 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.

Submit

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 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.

Submit

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 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.

Submit

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 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.

Submit

8) 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.

Submit

9) 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.

Submit

10) 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.

Submit

11) 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.

Submit

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.

Submit

13) 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.

Submit

14) 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.

Submit

15) 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.

Submit

16) 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.

Submit

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.

Submit

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.

Submit

19) 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.

Submit

20) 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.

Submit

21) 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.

Submit

22) 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.

Submit

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.

Submit

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.

Submit

25) 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.

Submit

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.

Submit

27) 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.

Submit

28) 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.

Submit

29) 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.

Submit

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.

Submit
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