What is the length of AC ?

Options

A. `2.94`
B. `3.49`
C. `3.81`
D. `4.05`

Answer

A

Explanation

It's a right triangle, so the acute angles add up to 90 degrees. Since their degree measures are in a 2 - to 3 ratio, they must be `(2)/(5)` of 90 `(3)/(5)` of 90, or 36 and 54 :

The side AC you're looking for is opposite the `36^(@)` angle. Therefore,
`(AC)/(5)=sin 36^(@)`
Use your calculator to find that `sin 36^(@)~~0.588`. Therefore,
`(AC)/(5)~~0.588`
`AC~~5(0.588)=2.94`