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

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.

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

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

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

$42=6\times base$

$base=7$

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

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.

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

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

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

√8

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

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

4.5

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

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

Explanation

We can use the Pythagorean Theorem to solve for x.

92 + _x_2 = 152

81 + _x_2 = 225

_x_2 = 144

x = 12

Points $\dpi{100} \small A$ , $\dpi{100} \small B$ , and $\dpi{100} \small C$ are collinear (they lie along the same line). $\angle ACD = 90^{\circ}$ , $\angle CAD=30^{\circ}$ , $\angle CBD=60^{\circ}$ , $\overline{AD}=4$

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