Question

Solve for x in the triangle. Round your answer to the nearest tenth.
37°

Answer 1

x = 7.2 units

Explanation:

Because this is a right triangle, we can use trigonometric functions to solve for variable x. We are given an adjacent leg to our triangle, an acute angle, and the hypotenuse so we are going to take the cosine of that angle.

Cosine of an angle equals the adjacent leg divided by the hypotenuse so our equation looks like:
cos 37° =
`(x)/(9)`

To isolate variable x we are going to multiply both sides by 9:
9(cos 37°) = 9(
`(x)/(9)`)

Multiply and simplify:
9 cos 37° = 9x / 9
9 cos 37° = 1x
9 cos 37° = x

Break out a calculator and solve, making sure to round to the nearest tenth as the directions say:
x = 7.2