Unit 4 Right Triangles, Pythagorean Theorem Practice Test
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.
- 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. 48Explanation
8*12/2 = 48Rate this question:
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- 2.
Find the missing side of the right triangle below. Round to the nearest tenth.You need to use Pythagorean Theorem.
Correct Answer
14.4Explanation
8^2 + 12^2 = c^2
64 + 144 = c^2
208 = c^2
sqrt(208)= 14.4 to the nearest tenth.Rate this question:
- 3.
Find the area of a rectangle that has a base of 12 and a height of 8.
Correct Answer
96Explanation
12*8 = 96Rate this question:
- 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
10Explanation
the diagonal is the hypotenuse.
6^2 + 8^2 = c^2
36 + 64 = c^2
100 = c^2
sqrt(100) = 10 = diagonalRate this question:
- 5.
Find the missing side of the right triangle below.
Correct Answer
7Explanation
24^2 + b^2 = 25^2
576 + b^2 = 625
-576 -576
b^2 = 49
b = sqrt(49) = 7Rate this question:
- 6.
Now find the area of the triangle. Use your answer from the last problem for the base of the triangle.
Correct Answer
84Explanation
7*24/2 = 84Rate this question:
- 7.
Find the missing side of the 45-45-90 triangle below.
Correct Answer
5Explanation
You are looking for the "x" side.Rate this question:
- 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. CExplanation
x = 8, so the hypotenuse has to be 8*sqrt(2)Rate this question:
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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 feetExplanation
The ladder is the hypotenuse so it should be 20*sqrt(2)Rate this question:
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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. DExplanation
x = 8, so the 2x side = 2*8 = 16Rate this question:
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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. EExplanation
You are missing the xsqrt(3) side and x = 8, so it should be 8*sqrt(3)Rate this question:
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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. BExplanation
8 = 2x, so x = 4Rate this question:
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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. 15/17Explanation
Pythagorean Thm - hypotenuse = 17, then Sin = o/h = 15/17Rate this question:
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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. 8/15Explanation
tan(B) - notice o and a switched. Tan(B) = o/a = 8/15Rate this question:
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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. CExplanation
The 1 is opposite the 30 degree angle and the sqrt(3) is adjacent.Rate this question:
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- 16.
Find Cos(60)
- A.
A
- B.
B
- C.
C
- D.
D
- E.
E
Correct Answer
A. AExplanation
The 1 is adjacent to the 60 degree angle and the 2 is the hypotenuseRate this question:
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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 milesExplanation
tan(20) = x/3. Cross multiply and x = 3tan(20) = about 1.1 miles.Rate this question:
- 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 feetExplanation
Sin(50) = 15/x Cross multiply and you get xSin(50) = 15, then divide and you get x = 15/Sin(50) = 19 feet approximately.Rate this question:
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Mar 17, 2023Quiz Edited by
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Mar 18, 2010Quiz Created by
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