Question

The pilot in a plane is cruising at 4 miles sees a tree. The angle of elevation from the base of the tree to the plane is 40°.

Answer 1

We have to find x.

We can use the trigonometric relations to find the value of x.

We know that, for a right triangle, the sine of an angle is equal to the quotient between the opposite side and the hypotenuse.

In this case, the opposite side of the angle is the height of the plane (4 mi) and the hypotenuse is x, so we can write:

`\begin{gathered} \cos (40\degree)=\frac{\text{Opposite}}{\text{Hypotenuse}}=(4)/(x) \\ x=(4)/(\cos (40\degree))\approx(4)/(0.766)\approx5.22 \end{gathered}`

Answer: the value of x is approximately 5.22 miles.