Question

1. A ship left port A heading for port B. It sailed due East for 40 miles. It then sailed due North

for 30 miles. Find:

i. The distance between the two ports

ii. The bearing of port B as measured from port A

iii. The bearing of port A as measured from port B
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Answer 1

i)Distance between port A and Port B is 500 miles.

ii)Bearing of port B from A= N 53.13°E

iii)Bearing of port A from B= S 53.13°W

Explanation:

The movement of the ship from port A to port B formed a right angle triangle.

To calculate the distance from port A to post B,

Let distance AB = X

AC = y

CB= z

X² = y² + z²

x² = 40² + 30²

= 1600+900

= 2500

X²= 2500

X= 50

Distance between port A and Port B is 500 miles.

Angle at A

30/sin a= 50/sin 90

Sin a = 30/50

a= sin^-1( 0.6)

a= 36.87°

Bearing of port B from A

90-36.87= 53.13

Bearing of port B from A= N 53.13°E

Angle at B

=180-(90+36.87)

b= 53.13°

Bearing of port A from B= S 53.13°W