# Applications of Trigonometry Heights and Distances Chapter 9 Exercise 9.1 Question 7

Applications of Trigonometry Heights and Distances Chapter 9 Exercise 9.1 Question 7

7.      From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45$^\circ$ and 60$^\circ$ respectively. Find the height of the tower.

Solution:

It is given that tower (AD) is fixed at the top of 20 m high building (DC).

In $\triangle BDC$, we have

$\frac{DC}{BC} =tan 45^\circ$

$\Rightarrow DC = BC$

$\Rightarrow BC = 20$ m

In $\triangle ABC$, we have

$\frac{AC}{BC}=tan 60^\circ$

$\Rightarrow AC= BCtan 60^\circ = 20\sqrt{3}$ m

Length of tower (AD) = AC - DC = $20\sqrt{3} - 20 = 20(\sqrt{3}-1)$ m

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