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.

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

Hence

Using calculator

Approximately

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

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

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47