Unit 4 Right Triangles, Pythagorean Theorem Practice Test

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Quizzes Created: 29 | Total Attempts: 19,181

Questions: 18 | Attempts: 693 | Updated: Mar 17, 2023

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Unit 4 Right Triangles, Pythagorean Theorem Practice Test - Quiz

This quiz will test you on right triangles (triangles in which one angle is 90 degrees) and the Pythagorean theory, which states that the square of the hypotenuse is equal to the sum of the squares of the other sides.

Questions and Answers

1.

Find the area of a triangle that has a base of 12 and a height of 8.
- A.
  
  96
- B.
  
  48
- C.
  
  20
- D.
  
  192
- E.
  
  Cannot be determined
Correct Answer
B. 48

Explanation
8*12/2 = 48

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0
2
2.

Find the missing side of the right triangle below. Round to the nearest tenth.You need to use Pythagorean Theorem.

Correct Answer
14.4

Explanation
8^2 + 12^2 = c^2
64 + 144 = c^2
208 = c^2
sqrt(208)= 14.4 to the nearest tenth.

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1
4 0
3.

Find the area of a rectangle that has a base of 12 and a height of 8.

Correct Answer
96

Explanation
12*8 = 96

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1
4 1
4.

Find the length of the diagonal of a rectangle that has a length of 6 and a width of 8. You need to draw the rectangle. The diagonal cuts it in half (use Pythagorean theorem).

Correct Answer
10

Explanation
the diagonal is the hypotenuse.
6^2 + 8^2 = c^2
36 + 64 = c^2
100 = c^2
sqrt(100) = 10 = diagonal

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4
5.

Find the missing side of the right triangle below.

Correct Answer
7

Explanation
24^2 + b^2 = 25^2
576 + b^2 = 625
-576 -576
b^2 = 49
b = sqrt(49) = 7

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4
6.

Now find the area of the triangle. Use your answer from the last problem for the base of the triangle.

Correct Answer
84

Explanation
7*24/2 = 84

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4
7.

Find the missing side of the 45-45-90 triangle below.

Correct Answer
5

Explanation
You are looking for the "x" side.

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4
8.

Which is the length of the missing side of the 45-45-90 triangle below?
- A.
  
  A
- B.
  
  B
- C.
  
  C
- D.
  
  D
- E.
  
  E
Correct Answer
C. C

Explanation
x = 8, so the hypotenuse has to be 8*sqrt(2)

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9.

A ladder leans against a house at a 45 degree angle. If the ladder reaches 20 feet high on the house, how long is the ladder to the nearest tenth of a foot?
- A.
  
  28.3 feet
- B.
  
  14.1 feet
- C.
  
  34.6 feet
- D.
  
  40 feet
- E.
  
  10 feet
Correct Answer
A. 28.3 feet

Explanation
The ladder is the hypotenuse so it should be 20*sqrt(2)

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10.

Find the missing side of the 30-60-90 triangle below.
- A.
  
  A
- B.
  
  B
- C.
  
  C
- D.
  
  D
- E.
  
  E
Correct Answer
D. D

Explanation
x = 8, so the 2x side = 2*8 = 16

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11.

Find the missing side of the 30-60-90 triangle below.
- A.
  
  A
- B.
  
  B
- C.
  
  C
- D.
  
  D
- E.
  
  E
Correct Answer
E. E

Explanation
You are missing the xsqrt(3) side and x = 8, so it should be 8*sqrt(3)

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12.

Find the missing side of the 30-60-90 triangle below.
- A.
  
  A
- B.
  
  B
- C.
  
  C
- D.
  
  D
- E.
  
  E
Correct Answer
B. B

Explanation
8 = 2x, so x = 4

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13.

What is Sin(A)(You need to find the hypotenuse first)
- A.
  
  15/8
- B.
  
  8/15
- C.
  
  15/17
- D.
  
  8/17
- E.
  
  17.15
Correct Answer
C. 15/17

Explanation
Pythagorean Thm - hypotenuse = 17, then Sin = o/h = 15/17

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14.

Find Tan(B)
- A.
  
  15/8
- B.
  
  8/15
- C.
  
  15/17
- D.
  
  8/17
- E.
  
  17/15
Correct Answer
B. 8/15

Explanation
tan(B) - notice o and a switched. Tan(B) = o/a = 8/15

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15.

Find Tan(30)*Use the special right triangle*.
- A.
  
  A
- B.
  
  B
- C.
  
  C
- D.
  
  D
- E.
  
  E
Correct Answer
C. C

Explanation
The 1 is opposite the 30 degree angle and the sqrt(3) is adjacent.

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16.

Find Cos(60)
- A.
  
  A
- B.
  
  B
- C.
  
  C
- D.
  
  D
- E.
  
  E
Correct Answer
A. A

Explanation
The 1 is adjacent to the 60 degree angle and the 2 is the hypotenuse

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17.

A car spots a mountain off in the distance at an angle of elevation of 20 degrees. The car is 3 miles from the mountain. How high is the mountain to the nearest tenth of a mile?

Correct Answer
1.1
1.1 miles

Explanation
tan(20) = x/3. Cross multiply and x = 3tan(20) = about 1.1 miles.

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4
18.

A ladder leans against a house at an angle of elevation of 50 degrees. How long is the ladder if it reaches a height of 15 feet on the side of the house? Round to the nearest foot.

Correct Answer
19
19 feet

Explanation
Sin(50) = 15/x Cross multiply and you get xSin(50) = 15, then divide and you get x = 15/Sin(50) = 19 feet approximately.

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4

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Current Version
Mar 17, 2023

Quiz Edited by
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Mar 18, 2010

Quiz Created by
Annacabral

Unit 4 Right Triangles, Pythagorean Theorem Practice Test

Find the area of a triangle that has a base of 12 and a height of 8.

Find the missing side of the right triangle below. Round to the nearest tenth.You need to use Pythagorean Theorem.

Find the area of a rectangle that has a base of 12 and a height of 8.

Find the length of the diagonal of a rectangle that has a length of 6 and a width of 8. You need to draw the rectangle. The diagonal cuts it in half (use Pythagorean theorem).

Find the missing side of the right triangle below.

Now find the area of the triangle. Use your answer from the last problem for the base of the triangle.

Find the missing side of the 45-45-90 triangle below.

Which is the length of the missing side of the 45-45-90 triangle below?

A ladder leans against a house at a 45 degree angle. If the ladder reaches 20 feet high on the house, how long is the ladder to the nearest tenth of a foot?

Find the missing side of the 30-60-90 triangle below.

Find the missing side of the 30-60-90 triangle below.

Find the missing side of the 30-60-90 triangle below.

What is Sin(A)(You need to find the hypotenuse first)

Find Tan(B)

Find Tan(30)*Use the special right triangle*.

Find Cos(60)

A car spots a mountain off in the distance at an angle of elevation of 20 degrees. The car is 3 miles from the mountain. How high is the mountain to the nearest tenth of a mile?

A ladder leans against a house at an angle of elevation of 50 degrees. How long is the ladder if it reaches a height of 15 feet on the side of the house? Round to the nearest foot.

Find Tan(30)Use the special right triangle.