Question

A plane is 112 mi north and 172 mi east of an airport. Find x, the angle the pilot should turn in order to fly directly to thealrport. Round your answer to the nearest tenth of a degree.

Answer 1

Given:

The horizontal distance between plane and the airport is, 172 miles.

The vertical distance between plane and the airport is, 112 miles.

The objective is to find the angle x the pilot should turn in order to fly directly to the

alrport.

Consider the given figure as,

Here, C represents the position of plane and A represents the position of airport.

By considering angle x, the opposite side of right triangle is AB and the adjacent side is BC.

Now, the angle x can be calculated using trigonometric ratio of tanθ.

`\begin{gathered} \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \\ \tan x=(112)/(172) \\ x=\tan ^(-1)((112)/(172)) \\ x=33.1\degree \end{gathered}`

Hence, the angle the pilot should turn in order to fly directly to the

alrport is 33.1°.