Question

A plane is 142 km north and 166 km east of an airport. Find x, the angle the pilot should turn in order to fly directly to the airport. Round your answer to the nearest tenth of a degree.

Answer 1

Given:

A plane is 142 km north and 166 km east of an airport as shown in the given figure.

To find:

The value of x to the nearest tenth of a degree.

Solution:

In a right angle triangle,

$\tan \theta=\dfrac{Perpendicular}{Base}$

It is also written as

$\tan \theta=\dfrac{Opposite}{Adjacent}$

For the given triangle,

$\tan x=\dfrac{142}{166}$

$\tan x=\dfrac{71}{83}$

$x=\tan^{-1} \dfrac{71}{83}$

$x\approx 40.5$

Therefore, the value of x is 40.5 degrees.