The angles of elevation of the top of a tower standing on a horizontal plane from two points on a line passing through the foot of the tower at distances 49 m and 36 m are 43^ and 47^ respectively. What is the height of the tower?

Step-by-step solution

aligned & AB = h (height of the tower) & BD =36 ~m & BC =49 ~m & D =47^ & C =43^ aligned Now, in A B D , 47^ = h 36 ~m ...(i) and in ABC , aligned & 43^ = h 49 ~m & (90^ -47^ )= h 49 aligned 47^ = h 49 ...(ii) Multiplying equations (i) and (ii) aligned & 47^ 47^ = h 36 h 49 =1= h ^2 36 49 & ~h =6 7=42 ~m aligned Option (B) is correct