One leg of a right triangle is 9 units long . The hypotenuse of this triangle is 15 units long. What is the length of the other leg?

Question

One leg of a right triangle is 9 units long . The hypotenuse of this triangle is 15 units long. What is the length of the other leg?

2 Answers

Impact of this question

2353 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-19T02:17:13

12 units

Explanation:

Using Pythagorean theorem, $a^{2} + b^{2} = c^{2}$ $a^2 + b^2 = c^2$ , insert 15 as c because it is the hypotenuse (c is always the hypotenuse or the longest side), and 9 as a.

$9^{2} + b^{2} = 15^{2}$ $9^2 + b^2 = 15^2$
81 + $b^{2}$ $b^2$ = 225
$b^{2}$ $b^2$ = 144
$\sqrt{b^{2}}$ $sqrt(b^2)$ = $\sqrt{144}$ $sqrt(144)$
b = 12 units

Answer 2 · 2018-03-19T12:21:29

See a solution process below:

Explanation:

The Pythagorean Theorem states, for a right triangle:

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

$a$ $a$ and $b$ $b$ are the legs of the right triangle
- $c$ $c$ is the hypotenuse of the right triangle

Substituting for $a$ $a$ and $c$ $c$ and solving for $b$ $b$ gives:

$9^{2} + b^{2} = 15^{2}$ $9^2 + b^2 = 15^2$

$81 + b^{2} = 225$ $81 + b^2 = 225$

$81 - 81 + b^{2} = 225 - 81$ $81 - color(red)(81) + b^2 = 225 - color(red)(81)$

$0 + b^{2} = 144$ $0 + b^2 = 144$

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

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

$b = 12$ $b = 12$

The other leg is 12 units long

Science

Math

Humanities

... and beyond

One leg of a right triangle is 9 units long . The hypotenuse of this triangle is 15 units long. What is the length of the other leg?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question