The hypotenuse of a right triangle is 15 centimeters long. One leg is 9 cm long. How do you find the length of the other leg?

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The hypotenuse of a right triangle is 15 centimeters long. One leg is 9 cm long. How do you find the length of the other leg?

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Answer 1 · 2018-03-22T00:07:45

The other leg is $12 cm$ $"12 cm"$ long.

Explanation:

Use the Pythagorean theorem:

$c^{2} = a^{2} + b^{2}$ $c^2=a^2+b^2$ ,

where:

$c$ $c$ is the hypotenuse, and $a$ $a$ and $b$ $b$ are the other two sides (legs).

Let $a = 9 cm$ $a="9 cm"$

Rearrange the equation to isolate $b^{2}$ $b^2$ . Plug in the values for $a$ $a$ and $c$ $c$ , and solve.

$b^{2} = c^{2} - a^{2}$ $b^2=c^2-a^2$

$b^{2} = {(15 cm)}^{2} - {(9 cm)}^{2}$ $b^2=("15 cm")^2-("9 cm")^2$

Simplify.

$b^{2} = {225 cm}^{2} - 81 {cm}^{2}$ $b^2="225 cm"^2-81 "cm"^2"$

$b^{2} = {144 cm}^{2}$ $b^2="144 cm"^2"$

Take the square root of both sides.

$b = \sqrt{{144 cm}^{2}}$ $b=sqrt("144 cm"^2")$

Simplify.

$b = 12 cm$ $b="12 cm"$

Answer 2 · 2018-03-22T00:08:31

$12$ $12$ centimeters long.

Explanation:

Since this is a right triangle, we can use the Pythagorean Theorem.

![https://www.onlinemathlearning.com/http://pythagorean-theorem.html](https://useruploads.socratic.org/yddUfckQ0We097UVMQGA_displayImage.aspx.jpg)
$c = hypotenuse$ $"c = hypotenuse"$
$a = leg$ $"a = leg"$
$b = leg$ $"b = leg"$

We can substitute in $c$ $c$ (the hypotenuse) and $a$ $a$ (one of the legs) to find the length of $b$ $b$ (the other leg)
$a^{2} + b^{2} = c^{2}$ $a^2 + b^2 = c^2$
$9^{2} + b^{2} = 15^{2}$ $9^2 + b^2 = 15^2$
$81 + b^{2} = 225$ $81 + b^2 = 225$
$b^{2} = 144$ $b^2 = 144$
$b = \sqrt{144}$ $b = sqrt144$
$b = 12$ $b = 12$

So the other leg is $12$ $12$ centimeters long.

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The hypotenuse of a right triangle is 15 centimeters long. One leg is 9 cm long. How do you find the length of the other leg?

2 Answers

Explanation:

Explanation:

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