Question

A bird is flying from A towards B at an angle of 35°, a point 30 km away from A. At B it changes its course of flight and heads towards C on a bearing of 48° and distance 32 km away. How far is B to the North of A?

(sin 55° = 0.8192, cos 55° = 0.5736, sin 42° = 0.6691, cos 42° = 0.7431)

Answer 1

Given:

A bird is flying from A towards B at angle of 35°, a point 30 km away from A so,

∠BAC = 35°

AB = 30 km

Heads towards Con, a bearing of 48° an distance 32 km away so,

∠EBD = 48°

EB = 32 km

values,

sin 55° = 0.8192

cos 55° = 0.5736

sin 42° = 0.6691

cos 42° = 0.7431

Hence,

`sintheta = (Upp)/(hyp)`

`costheta = (adj)/(hyp)`

i) Far is B to the North A .

⇒ sin 55° `= (AC)/30`

AC = 0.8192 × 30

= 24.58 km

ii) Far is B to the West of A

⇒ cos 55° `= (BC)/30`

BC = 0.5736 × 30

= 17.21 km

iii) Far is C to the East of B

⇒ cos 42° `= (DE)/32`

DE = 0.7431 × 32

= 23.78 km