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The position of three ships P,Q and R at sea are illustrated in the diagram. The...

Question

The position of three ships P,Q and R at sea are illustrated in the diagram. The arrows indicated the North direction. The bearing of Q from P is 050o and < PQR = 72o. Calculate the bearing of R and Q.

A) 155o

B) 80o

C) 158o

D) 91o

Explanation:

< NPQ = < PQB = 50$$^{\circ}$$(alt. < s)
< PQB = 50$$^{\circ}$$
< PQR = < PQR < PQB + < QBR = 72$$^{\circ}$$
< QBR = < PQR - < PQB = 72$$^{\circ}$$ - 50$$^{\circ}$$
= 22$$^{\circ}$$
< NQR = 180 - < QBR = 180$$^{\circ}$$ - 22 = 158$$^{\circ}$$, the bearing of R from Q = 158$$^{\circ}$$

Dicussion (1)

• < NPQ = < PQB = 50$$^{\circ}$$(alt. < s)
< PQB = 50$$^{\circ}$$
< PQR = < PQR < PQB + < QBR = 72$$^{\circ}$$
< QBR = < PQR - < PQB = 72$$^{\circ}$$ - 50$$^{\circ}$$
= 22$$^{\circ}$$
< NQR = 180 - < QBR = 180$$^{\circ}$$ - 22 = 158$$^{\circ}$$, the bearing of R from Q = 158$$^{\circ}$$