Answer to Question #169653 in Trigonometry for Surendra Singh

Question

The angle of elevation from ground to the top of building and to the top of chimney which is at the top of building are x0 and 450 respectively. The height of building is h. What is height of chimney in meters?

Answer 1

Solution.

Let $t$ meters be the height of chimney. Since the angle of elevation from ground to the top of chimney is $45^°,$ then distance to building is $(x+h)$ meters.

Since the angle of elevation from ground to the top of building is $x^°,$

then

$$\tan{x}=\frac{h}{t+h},$$

$$t=\frac{h}{\tan x}-h=\frac{h(1-\tan x)}{\tan x}.$$

Answer. $\frac{h(1-\tan x)}{\tan x}$ meters.