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
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