Question

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

Answer 1

Given:

The figure of a right angle triangle, we hypotenuse $\sqrt{113}$ mi and perpendicular 9 mi.

To find:

The length of the unknown leg in the right triangle.

Solution:

According to the Pythagoras theorem,

$Hypotenuse^2=Perpendicular^2+Base^2$

Using Pythagoras theorem, we get

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

$113=81+a^2$

$113-81=a^2$

$32=a^2$

Taking square root on both sides.

$\sqrt{32}=a$

It is only positive because the side length cannot be negative.

The length of the unknown leg in the right triangle is $\sqrt{32}$ mi.

Therefore, the correct option is B.