Question

A golfer at G wishes to hit a shot between two trees P and Q, as shown in the

diagram to the right. The trees are 31 metres apart, and the golfer is 74 metres
from P and 88 metres from P. Find the angle within which the golfer must play
the shot, correct to the nearest degree.

Answer 1

20°

Explanation:

You want the measure of angle G in triangle GPQ with side lengths GP=74, PQ=31, QG=88 meters.

Law of cosines

The law of cosines tells you the relevant relationship is ...

PQ² = GP² +GQ² -2·GP·GQ·cos(G)

Solving for angle G gives ...

G = arccos((GP² +GQ² -PQ²)/(2·GP·GQ))

G = arccos((74² +88² -31²)/(2·74·88)) = arccos(12259/13024)

G ≈ 19.735° ≈ 20°

The golfer must play the shot within an angle of about 20°.