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

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Example Questions

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 #2 : 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:

14, 48, 50

8, 15, 17

5, 7, 10

5, 12, 13

12, 16, 20

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 #3 : 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

4, 6, 9

6, 7, 8

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:

33√2

12 √6

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:

2 hours and 30 minutes

4 hours and 0 minutes

3 minutes and 20 seconds

3 minutes and 50 seconds

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 #4 : 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 #1 : 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:

$5$

$9$

$7$

$11$

$6$

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 #82 : Triangles

Triangle

$\left ( \bigtriangleup ABC \textup{ is a right triangle where } \angle B \textup{ is a right angle}\right)$

If $\angle A=30^{\circ}$ and $\overline{AB}=4$ , what is the length of $\overline{BC}$ ?

Possible Answers:

$\frac{4}{3}$

$\frac{4\sqrt{3}}{3}$

Correct answer:

$\frac{4\sqrt{3}}{3}$

Explanation:

AB is the leg adjacent to Angle A and BC is the leg opposite Angle A.

Since we have a $30^{\circ}-60^{\circ}-90^{\circ}$ triangle, the opposites sides of those angles will be in the ratio $x-x\sqrt{3}-2x$ .

Here, we know the side opposite the sixty degree angle. Thus, we can set that value equal to $x\sqrt{3}$ .

$4=x\sqrt{3}$

$\frac{4}{\sqrt{3}}=\frac{x\sqrt{3}}{\sqrt{3}}$

$\frac{4}{\sqrt{3}}\cdot \frac{\sqrt{3}}{\sqrt{3}}=x$

$x=\frac{4\sqrt{3}}{3}$

which also means

$\overline{BC}=\frac{4\sqrt{3}}{3}$

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Example Question #81 : Triangles

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

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

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 #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 #4 : 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 #82 : Triangles

Example Question #81 : Triangles

All PSAT Math Resources

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