Question

Solve a ship leave port and travel 21km on a bearing of 032° and then 45km on a bearing 287 calculate the distance and bearing of the port from the ship

Answer 1

Explanation:

Let shall be considering the Cosine rule in this situation.

a^2 = b^2+c^2- 2bc.cosA

Where a = ?

b = 21km

c 45km

A = 131

a^2 = 21^2+45^2-2(21*45).cos131

a^2 = 441+2025-1890(-0.6560)

a^2 = 2466+1239.951

a^2 = 3705.951

a= 60.876km

Finding the bearing of the port from the ship.

We shall be considering the Sine rule

Sin A/a = Sin B/b

Where A = ?

a = 45km

B = 131°

b = 60.876km

Sin A/45 = sin131/60.876

SinA×60.876 = 45×sin131

SinA×60.876= 45×0.7547

SinA×60.876 = 33.961

SinA= 33.961/60.876

SinA = 0.5578

A = sin^-1 0.5578

A = 33.9°