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