Question

An aeroplane flies 138 km in a southerly direction from a military air base to a drop-off point The drop-off point is 83 km west of the the bearing, correct to the nearest air base. Find degree, of:
A) the drop-off point from the air base
B) the air base from the drop-off point.

Answer 1

We are given: 

138 km south 
83 km west of the bearing is the drop-off point.

First, we need to illustrate the problem to clearly see the pattern.

A triangle is formed, 138 km down, then 83 km left. 

c^2 = 138^2 + 83^2 
c = 161.04 km

The angles are determined using Pythagorean Theorem:

a) 217 degrees 
b) 31 degrees

Answer 2

Answer:

A) the drop-off point from the air base : 31°  towards South West

B) the air base from the drop-off point : 59° towards North East

Step-by-step explanation:

Please refer to the image attached to the answer. Here we see that the Air base , The drop-off point and the south direction makes an right angle Triangle.

We are asked to find the angles x and y as shown in the figure. We use trigonometric ratios to determine them.

We know that in a right Triangle

$\tan \theta=\frac{opposite}{adjacent}$

Hence

$\tan x=\frac{83}{138}$

$\tan x = 0.60$

$x=\tan^{-1} (0.60)$

Using calculator

$x=30.96$

$x=31$ Approximately

Also the sum of all the angles in a right triangle is 90°. hence

$y=180-90-31$

$y=59$

hence we have our x and y as 31° and 59°