In the right triangle in Figure, If `theta = 42^(@)`, what is the value of x ?

Options

A. `4.9`
B. `5.8`
C. `6.7`
D. `8.1`

Answer

C

Explanation

The `42^(@)` angle is opposite the given 6, and the side you're looking for is the adjacent side, so you can use the tangent to find x.
`"tan"=("opposite")/("adjacent")`
tan `42^(@)=(6)/(x)`
`x=(6)/(tan 42^(@))`
Now, nobody expects you to know the tan of `42^(@)` from memory. This is one of those situations in which you have to use your calculator. Punch in `''6//tan 42^(@)''` (make sure that your calculator is in degree mode), and you'll get something like `6.663675089`, which is close to (C ).