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High School 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 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 #21 : Triangles

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 #101 : Geometry

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:

3 minutes and 20 seconds

2 hours and 30 minutes

4 hours and 0 minutes

1 hour and 45 minutes

3 minutes and 50 seconds

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 #101 : 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:

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

$\frac{4}{3}$

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 #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 #11 : How To Find The Length Of The Side Of A Right Triangle

Solve for $\small x$ .

Possible Answers:

Correct answer:

Explanation:

Use the Pythagorean Theorem to solve for the missing side of the right triangle.

a^2+b^2=c^2

In this triangle, $\small a=x,\ b=12,\ c=15$ .

x^2+12^2=15^2

Now we can solve for $\small x$ .

x^2+144=225

x^2=81

x=9

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Example Question #12 : How To Find The Length Of The Side Of A Right Triangle

Solve for $\small x$ .

Possible Answers:

110

$110\sqrt3$

$110\sqrt2$

$55\sqrt2$

Correct answer:

110

Explanation:

This image depicts a 30-60-90 right triangle. The length of the side opposite the smallest angle is half the length of the hypotenuse.

$a^2+b^2=c^2\rightarrow (a)^2+(a\sqrt{3})^2=(2a)^2$

2a=220

$a=\frac{220}{2}=110$

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Example Question #13 : How To Find The Length Of The Side Of A Right Triangle

Given a right triangle, solve for the missing leg if one leg is 12 and the hypotenuse is 13.

Possible Answers:

17.69

Correct answer:

Explanation:

Since the traingle is a right traingle, we can use the Pythagorean Theorem to solve for the missing leg:

a^2 + b^2 = c^2

a=12 and the hypotenuse c=13

(12)^2 + b^2 = (13)^2

b^2 = (13)^2- (12)^2

b^2 = 169- 144

b^2 = 25

b = 5

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

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

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

Example Question #21 : Triangles

Example Question #101 : Geometry

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 #101 : Triangles

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

Example Question #11 : How To Find The Length Of The Side Of A Right Triangle

Example Question #12 : How To Find The Length Of The Side Of A Right Triangle

Example Question #13 : How To Find The Length Of The Side Of A Right Triangle

All High School Math Resources

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