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SAT Math : How to find the length of the side of a right triangle

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Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

A right triangle has one side equal to 5 and its hypotenuse equal to 14. Its third side is equal to:

Possible Answers:

14.87

171

13.07

Correct answer:

13.07

Explanation:

The Pythagorean Theorem gives us a² + b² = c² for a right triangle, where c is the hypotenuse and a and b are the smaller sides. Here a is equal to 5 and c is equal to 14, so b² = 14² – 5² = 171. Therefore b is equal to the square root of 171 or approximately 13.07.

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Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

Which of the following could NOT be the lengths of the sides of a right triangle?

Possible Answers:

8, 15, 17

12, 16, 20

5, 7, 10

5, 12, 13

14, 48, 50

Correct answer:

5, 7, 10

Explanation:

We use the Pythagorean Theorem and we calculate that 25 + 49 is not equal to 100.
All of the other answer choices observe the theorem a² + b² = c²

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Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

Which set of sides could make a right triangle?

Possible Answers:

9, 12, 15

10, 12, 16

6, 7, 8

4, 6, 9

Correct answer:

9, 12, 15

Explanation:

By virtue of the Pythagorean Theorem, in a right triangle the sum of the squares of the smaller two sides equals the square of the largest side. Only 9, 12, and 15 fit this rule.

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Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

A right triangle with a base of 12 and hypotenuse of 15 is shown below. Find x.

Screen_shot_2013-03-18_at_10.29.39_pm

Possible Answers:

5.5

3.5

4.5

Correct answer:

Explanation:

Using the Pythagorean Theorem, the height of the right triangle is found to be = √(〖15〗²–〖12〗²) = 9, so x=9 – 5=4

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Example Question #2 : How To Find The Length Of The Side Of A Right Triangle

A right triangle has sides of 36 and 39(hypotenuse). Find the length of the third side

Possible Answers:

12 √6

33√2

Correct answer:

Explanation:

use the pythagorean theorem:

a² + b² = c² ; a and b are sides, c is the hypotenuse

a² + 1296 = 1521

a² = 225

a = 15

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Example Question #3 : How To Find The Length Of The Side Of A Right Triangle

Bob the Helicopter is at 30,000 ft. above sea level, and as viewed on a map his airport is 40,000 ft. away. If Bob travels in a straight line to his airport at 250 feet per second, how many minutes will it take him to arrive?

Possible Answers:

4 hours and 0 minutes

3 minutes and 20 seconds

3 minutes and 50 seconds

2 hours and 30 minutes

1 hour and 45 minutes

Correct answer:

3 minutes and 20 seconds

Explanation:

Draw a right triangle with a height of 30,000 ft. and a base of 40,000 ft. The hypotenuse, or distance travelled, is then 50,000ft using the Pythagorean Theorem. Then dividing distance by speed will give us time, which is 200 seconds, or 3 minutes and 20 seconds.

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Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

A right triangle has two sides, 9 and x, and a hypotenuse of 15. What is x?

Possible Answers:

Correct answer:

Explanation:

We can use the Pythagorean Theorem to solve for x.

9² + x² = 15²

81 + x² = 225

x² = 144

x = 12

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Example Question #5 : How To Find The Length Of The Side Of A Right Triangle

The area of a right traingle is 42. One of the legs has a length of 12. What is the length of the other leg?

Possible Answers:

$6$

$7$

$11$

$5$

$9$

Correct answer:

$7$

Explanation:

$Area= \frac{1}{2}\times base\times height$

$42=\frac{1}{2}\times base\times 12$

$42=6\times base$

$base=7$

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Example Question #6 : How To Find The Length Of The Side Of A Right Triangle

Solve for x.

Possible Answers:

Correct answer:

Explanation:

Use the Pythagorean Theorem. Let a = 8 and c = 10 (because it is the hypotenuse)

$\small a^2+x^2=c^2$

$\small 8^2+x^2=10^2$

$\small 64+x^2=100$

$\small x^2=100-64=36$

$\small x=6$

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Example Question #7 : How To Find The Length Of The Side Of A Right Triangle

Solve each problem and decide which is the best of the choices given.

If $sin x =\frac{12}{13}$ , what is tan (x) ?

Possible Answers:

$tan(x)=\frac{12}{13}$

$tan(x)=\frac{5}{12}$

$tan(x)=\frac{13}{12}$

$tan(x)=\frac{12}{5}$

$tan(x)=\frac{5}{13}$

Correct answer:

$tan(x)=\frac{12}{5}$

Explanation:

This is a 5-12-13 triangle. We can find the value of the other leg by using the Pythagorean Theorem.

Remembering that

$sin=\frac{opposite}{hypotenuse}$ .

Thus,

a^2+12^2=13^2

a^2+144=169

a^2=25

a=5 .

If $sin(x)=\frac{12}{13}$ , you know the adjacent side is .

Thus, making

$tan(x)=\frac{opposite}{adjacent}=\frac{12}{5}$ because tangent is opposite/adjacent.

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SAT Math : How to find the length of the side of a right triangle

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

Example Question #2 : How To Find The Length Of The Side Of A Right Triangle

Example Question #3 : How To Find The Length Of The Side Of A Right Triangle

Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

Example Question #5 : How To Find The Length Of The Side Of A Right Triangle

Example Question #6 : How To Find The Length Of The Side Of A Right Triangle

Example Question #7 : How To Find The Length Of The Side Of A Right Triangle

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