Unit 4 Right Triangles, Pythagorean Theorem Practice Test

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1. Find the missing side of the right triangle below.

Explanation

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

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About This Quiz
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... see moreis equal to the sum of the squares of the other sides. see less

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

Explanation

12*8 = 96

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3. 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).

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. 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?

Explanation

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

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

Explanation

8*12/2 = 48

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

Explanation

You are looking for the "x" side.

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

Explanation

7*24/2 = 84

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

Explanation

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

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

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

Explanation

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

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

Explanation

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

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

Explanation

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

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13. Find Cos(60)

Explanation

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

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

Explanation

8 = 2x, so x = 4

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15. Find Tan(B)

Explanation

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

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

Explanation

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

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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?

Explanation

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

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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.

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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Find the missing side of the right triangle below.
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...
A ladder leans against a house at a 45 degree angle. If the ladder...
Find the area of a triangle that has a base of 12 and a height of 8.
Find the missing side of the 45-45-90 triangle below.
Now find the area of the triangle. Use your answer from the last...
Which is the length of the missing side of the 45-45-90 triangle...
Find the missing side of the right triangle below. Round to the...
Find the missing side of the 30-60-90 triangle below.
What is Sin(A)(You need to find the hypotenuse first)
Find the missing side of the 30-60-90 triangle below.
Find Cos(60)
Find the missing side of the 30-60-90 triangle below.
Find Tan(B)
Find Tan(30)*Use the special right triangle*.
A car spots a mountain off in the distance at an angle of elevation of...
A ladder leans against a house at an angle of elevation of 50 degrees....
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