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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.

Options

A) 155o

B) 80o

C) 158o

D) 91o

The correct answer is C.

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\(^{\circ}\)

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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\(^{\circ}\)

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