Please answer q 16. I reached the cot ? tan point but can't solve it further. Please explain in brackets side by side.

16.  The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complimentary. Prove that the height of the tower is 6 m. 
  Please answer q 16. I reached the cot ? tan point but cant solve it further. Please explain in brackets side by side.

Dear student,

Let height of the tower be h m. Given, the angles of elevation of the top of tower from the two points are complementary.   ACB = θ and ADB = 90-θ  In ABC, 

In ABD,

tan2θ=94tanθ=94tanθ=32                    --(neglecting the -ve value)
 Height of the tower = h = 4 tan θ = 4 ×32 =2×3= 6 m             (Using (1))  Thus, the height of the tower is 6 m.

Regards

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