Two forest fire stations, P and Q, are 20.0 km apart. A

ranger at station Q sees a fire 15.0 km away. If the angle

between the line PQ and the line from P to the fire is

how far, to the nearest tenth of a kilometre, is

station P from the fire?

Given that the angle is 25 degrees, we shall apply cosine rule to solve this question.

c^2=a^2+b^2-2abcosC

thus plugging the values we get:

15^2=x^2+20x^2-40xcos25

x^2-36.252x+175=0

thus solving the quadratic using quadratic formula we obtain:

x=[36.252+/-√614.208]/2

x=5.7 km or 30.5 km