Q)  From the top of a tower 100 m high, a man observes two cars on the opposite sides of the tower with angle of depression 30⁰ and 45⁰ respectively. Find the distance between the two cars. (use 3 = 1.73)

Ans: 

Let PQ be the tower, A and B the two cars, man observes the 2 cars from point P. Let angle of elevations and distances of cars from the tower be D₁ and D₂ as shown in the image above.

In Δ APQ, tan 30 =

D₁ = 100 √3  = 100 x 1.73 = 173 m

In Δ BPQ, tan 45 =

D₂ = 100 m

Hence, the distance between the both cars = D₁ + D₂ = 173 + 100 = 273 m

Therefore, the distance between the two cars is 273 m.