Question

A straight tunnel is to be made through a mountain. A surveyor observes the two extremities A and B of the tunnel to be built from a point P in front of the mountain. If AP = 3 km, BP = 5 km and ∠APB = 120° , then find the length of the tunnel to be built.

Answer 1

p² = a² + b² – 2ab cos P

p² = 9 + 25 – 30 Cos 120° 

p² = 9 + 25 – 30 (-1/2) = 34 + 15 = 49

⇒ p = √49 = 7 km