Question

If a right triangle's hypotenuse is 17 units long, and one of its legs is 15 units long, how long is the other leg?

Answer 1

8 units

Explanation:

Hello!

So, there's a formula we can apply to right-angled triangles: Pythagorean's theorem. It states that c =
`\sqrt{{a}^2 + b^(2) }`, where c is the hypotenuse and a and b are the legs of the triangle.

So, from the problem, if c = 17 and a = 15, then, we're solving for b. So we'll rewrite the theorem to solve for b.

`{c}^2 = {a}^2+{b}^2\\{c}^2-{a}^2={b}^2\\{b} = \sqrt{{c}^2-{a}^2}`

Okay, so now we have isolated the theorem for b. Let's plug in our values for c and a.

`b = \sqrt{{17}^2-{15}^2}\\b = √(289-225)\\b = √(64)\\b = 8`

So, using the theorem, we found b = 8. To check our work, let's plug in b and a and solve for c.

`c = \sqrt{{a}^2+{b}^2}}\\c = \sqrt{{15}^2+{8}^2}\\c = √(225+64)\\c = √(289)\\c = 17\\`

So, we got our hypotenuse to equal 17 units, which is correct! So, our b is correct too. Awesome