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

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

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=(opposite)/(adjacent)`

Hence

`\tan x=(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°