Question

What is the length of the unknown leg in the right triangle?

Answer 1

Pythagorean theorem: ⇒ a²+b²=c²

A unknown leg of a right triangle can be found using the Pythagorean theorem.

a²+b²=c²

a²+9²=√113²

You had to solve by the equation with exponents.

And it gave us ⇒ a²+81=113

And then you had to subtract by eighty-one (81) from both sides of equation form.

And it gave us ⇒ a²=32

And finally you had to used their square root with thirty-two (32) from both sides of equation form.

And it gave us ⇒ a²=32, $\sqrt{a^2}= \sqrt{32}$, and $a=\sqrt{32}$.

32 miles is the correct and final answer.

Hope this helps! And thank you for posting your question at here on brainly, and have a great day. -Charlie

Answer 2

So for this, we will be using the pythagorean theorem, which is $leg^2+leg^2=hypotenuse^2$ , to find the missing leg. Since we know that a and 9 are our legs and √113 is our hypotenuse, plug them into the equation as such:

$a^2+9^2=\sqrt{113}^2$

Firstly, solve the exponents:

$a^2+81=113$

Next, subtract 81 on both sides of the equation:

$a^2=32$

Next, square root both sides of the equation:

$a=\sqrt{32}$

Your final answer is √32 miles.