Question

Solve for x

Round to the nearest tenth

Answer 1

36.9°

Explanation:

Since this is a right triangle, the value of x can be found using trigonometric functions. Looking at the diagram, we are given the side length opposite the angle x and the side length adjacent to it.

To figure out which function is needed, use the trick of SOH-CAH-TOA. Since we are given both the opposite and adjacent sides, we can use tangent as indicated.

`tan(x) = (opposite)/(adjacent)`, so we can plug in the values. 9 is the opposite while 12 is the adjacent:

`tan(x) = (9)/(12)`

To solve for x we can use inverse tangent (arctan) on
`(9)/(12)`:

`x = tan^(-1)((9)/(12))`

Putting this into a calculator gets 36.869897646 degrees, which can be rounded to 36.9°.