Question

a window in a building is at a height of 10m above the ground.the angle of depression of a point P on the ground from the window is 30°. the angle of elevation of the top of the building from the point P is 60°. find the height of the buulding.

Answer 1

I think it is helpful for you

Answer 2

Answer:

29.99m

Step-by-step explanation:

Refer the attached figure

The window is 10 m above the ground i.e. BC = 10 m

Height of building = AC

The angle of depression of a point P on the ground from the window is 30° i.e. ∠BDC= 30°

The angle of elevation of the top of the building from the point P is 60°. i.e. ∠ADC= 60°

In ΔBDC

Using trigonometric ratio

$Tan\theta = \frac{Perpendicular}{Base}$

$Tan30^{\circ} = \frac{BC}{DC}$

$DC= \frac{10}{\frac{1}{\sqrt{3}}}$

$DC=17.32$

Now In ΔADC

Using trigonometric ratio

$Tan\theta = \frac{Perpendicular}{Base}$

$Tan90^{\circ} = \frac{AC}{DC}$

$\sqrt{3}= \frac{AC}{17.32}$

$\sqrt{3} \times 17.32= AC$

$29.99= AC$

Hence the height of the building is 29.99 m