Question

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

22 mi
32 mi
104 mi
194 mi

Answer 1

`√(32)` mi

Explanation:

For a right angled triangle, if the sides containing right angle is a and b then

hypotenuse to the triangle is given by hypotenuse =
`√(a^2+b^2)`

______________________

In the problem side containing right angle is 9 mi and a mi

while hypotenuse
`√(113)` mi.

Using formula for hypotenuse and using value 9 mi, a mi and
`√(113)` we have

`hypotenuse = √(a^2+b^2) \\=>√(113) = √(a^2+9^2) \\=>√(113) = √(a^2+81) / squaring/ both / side\\=> 113 = a^2+81\\=> 113 - 81 = a^2\\=> a^2 = 32\\=>a = √(32)`

Thus length of unknown leg is
`√(32)` mi.