Question

Find the value of x. Round lengths of segments to the nearest tenth andangle measures to the nearest degree.

Answer 1

7.8

Step-by-step explanation:

The length x, the side with length 6, and the angle of 40 degrees are related by the trigonometric function cosine, so

`\cos 40=(6)/(x)`

Because x is the hypotenuse and 6 is the adjacent side.

Solving for x, we get

`\begin{gathered} x\cos 40=x\cdot(6)/(x) \\ x\cos 40=6 \\ (xcos40)/(\cos40)=(6)/(\cos 40) \\ x=(6)/(\cos 40)=(6)/(0.766)=7.8 \end{gathered}`

Therefore, the value of x is 7.8