How to find the length of the side of a right triangle

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Math › How to find the length of the side of a right triangle

Questions 1 - 10
1

The legs of a right triangle are 8\ cm and 11\ cm. Rounded to the nearest whole number, what is the length of the hypotenuse?

14\ cm

15\ cm

10\ cm

9\ cm

2\ cm

Explanation

Use the Pythagorean Theorem. The sum of both legs squared equals the hypotenuse squared.

2

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?

7

5

6

9

11

Explanation

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

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

42=6\times base

base=7

3

Given a right triangle with a leg length of 6 and a hypotenuse length of 10, find the length of the other leg, x.

Act_math_106

8

16

4

64

Explanation

Using Pythagorean Theorem, we can solve for the length of leg x:

_x_2 + 62 = 102

Now we solve for x:

_x_2 + 36 = 100

_x_2 = 100 – 36

_x_2 = 64

x = 8

Also note that this is proportionally a 3/4/5 right triangle, which is very common. Always look out for a side-to-hypoteneuse ratio of 3/5 or 4/5, or a side-to-side ratio of 3/4, in any right triangle, so that you may solve such triangles rapidly.

4

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

33

42

15

12 √6

33√2

Explanation

use the pythagorean theorem:

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

a2 + 1296 = 1521

a2 = 225

a = 15

5

Given a right triangle with a leg length of 2 and a hypotenuse length of √8, find the length of the other leg, x.

Vt_triangle_x-2-sqrt8

2

6

√8

10

4

Explanation

Using Pythagorean Theorem, we can solve for the length of leg x:

_x_2 + 22 = (√8)2 = 8

Now we solve for x:

_x_2 + 4 = 8

_x_2 = 8 – 4

_x_2 = 4

x = 2

6

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

3.5

4

4.5

5

5.5

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

7

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

10

11

12

13

14

Explanation

We can use the Pythagorean Theorem to solve for x.

92 + _x_2 = 152

81 + _x_2 = 225

_x_2 = 144

x = 12

8

Triangles

Points \dpi{100} \small A, \dpi{100} \small B, and \dpi{100} \small C are collinear (they lie along the same line). , , ,

Find the length of segment \overline{BD}.

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

2\sqrt{3}

2

\frac{\sqrt{3}}{2}

\frac{2\sqrt{3}}{3}

Explanation

The length of segment \overline{BD} is \frac{4\sqrt{3}}{3}

Note that triangles \dpi{100} \small ACD and \dpi{100} \small BCD are both special, 30-60-90 right triangles. Looking specifically at triangle \dpi{100} \small ACD, because we know that segment \overline{AD} has a length of 4, we can determine that the length of segment \overline{CD} is 2 using what we know about special right triangles. Then, looking at triangle \dpi{100} \small BCD now, we can use the same rules to determine that segment \overline{BD} has a length of \frac{4}{\sqrt{3}}

which simplifies to \frac{4\sqrt{3}}{3}.

9

Solve for .

Question_9

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.

10

In a right triangle a hypotenuse has a length of 8 and leg has a length of 7. What is the length of the third side to the nearest tenth?

1.0

3.9

2.4

3.6

Explanation

Using the pythagorean theorem, 82=72+x2. Solving for x yields the square root of 15, which is 3.9

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