Consider a triangular plot A B C with sides A B = 7 m , B C = 5 m and C A = 6 m . A vertical lamp-post at the mid-point D of A C subtends an angle 30 ° at B . The height (in m ) of the lamp-post is:

Step-by-step solution

The length of the median B D is given by B D = 1 2 2 B C 2 + B A 2 - A C 2 ⇒ B D = 1 2   2 25 + 49 - 36 ⇒ B D = 1 2 112 ⇒ B D = 4 7 2 = 2 7   m . Now, let D T be the tower of height h   m and it subtends ∠ T B D = 30 ° at the vertex B . Then, in ∆ T D B we have tan ∠ T B D = T D B D ⇒ tan 30 ° = h 2 7 ⇒ 1 3 = h 2 7 ⇒ h = 2 7 3 ⇒ h = 2 3 21   m .