Two poles standing on a horizontal ground are of heights 5 m and 10 m respectively. The line joining their tops makes an angle of 15 ° with the ground. Then the distance ( in m ) between the poles, is

Step-by-step solution

Let, D C be the pole of height 5   m and A B be the pole of height 10   m . Also, let D M ⊥ A B , then A C D M is a rectangle and hence, A M = D C = 5   m and B M = A B - A M = 10 - 5 = 5   m and the distance between the poles is A C = M D = K   ( let ) . In Δ B D M t a n 15 ° = B M M D = 5 K ⇒ K = 5 t a n 15 ° ⇒ K = 5 3 + 1 3 - 1 × 3 + 1 3 + 1 ⇒ K = 5 3 + 1 + 2 3 3 - 1 ⇒ K = 5 2 + 3   m .