Bearing and distance

Question

Two ships A and B leave the same harbour at the same time in the directions 152° and 142° respectively. Calculate the distance between the two ships when A has travelled 10km and B has travelled 12km.what is the bearing of A from B at this time.

Answer 1

Hello Temmy,

First of all graph coordinate plane.

Then show the angle 152 that starts of x-axis then make the angle 142 also starts of x-axis

As a result you will have a triangle that 2 sides are 10 and 12 Km and angle between is 10 degree

152 - 142 = 10

The end of these vectors will be the position of ships

for finding the distance of two ships you need to use cosine law a^2 = b^2 + c^2 - 2bc cos(a)

(distance between two ships )^2 = 10^2 + 12^ 2 -2 *10*12 cos(10)

= 100 + 144 - 240 * .9848 = 7.6461

distance between 2 ship = √7.6461 = 2.7651 Km

I hope it is useful,

Minoo