Question

Find the value of x, rounded to the nearest tenth.

Answer 1

x= 36.2

Explanation:

Because that's a right triangle and the reference angle and adjacent side measures are given to us, we can use the trig ratio for cosine. Cosine relates the side adjacent to (next to...NOT ever the hypotenuse!) the angle to the hypotenuse. Therefore, our equation will look like this:

`cos(28)=(32)/(x)`

Solving for x we have

`x=(32)/(cos(28))`

Perform that operation on your calculator in degree mode and you'll get that the length of the hypotenuse is 36.2. If for some reason, your math gave you the length of the hypotenuse and it was shorter than one of the other sides, you did something wrong. The hypotenuse will ALWAYS be the longest side in a right triangle.