**Applications of Trigonometry Heights and Distances Chapter 9 Exercise 9.1 Question 16**

**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.

**Solution:**

It is given that and are complementary which means their sum is equal to .

Let and

It is given that BD = 4 m and BC = 9m which means DC = 9-4 = 5 m

In

** {tan(90-x) = cot x}**

** (1)**

In

**(2)**

From** (1) and (2)**, we can say that **9cot x=4tan x**

**(3)**

Putting equation** (3)** in equation** (2)**, we get

**m**

**Therefore, Height of the Tower is equal to 6 m**