Question

angle of elevation of the top of a cloud as observed from a 16 tall building is 60 degree and the angle of depression of a foot of a hill is 30 degree find the height of the cloud​

Answer 1

This question is based on the concept of Trigonometry.

Recall the formula:

$\sin \theta = \dfrac{\text{opposite}}{\text{hypothenuse}}$

$\cos \theta = \dfrac{\text{adjacent}}{\text{hypothenuse}}$

$\tan \theta = \dfrac{\text{opposite}}{\text{adjacent}}$

Find the distance between the foot of the hill and the building:

Let D be the distance between the foot of the hill and the building.

$\tan \theta = \dfrac{\text{opposite}}{\text{adjacent}}$

$\tan(30)= \dfrac{\text{D}}{16}}$

$D = 16 \times \tan(60)$

$D = 16\sqrt{3} \text{ units}$

Find the height of the cloud from the building:

Let H be the height of the cloud from the top of the building.

$\tan \theta = \dfrac{\text{opposite}}{\text{adjacent}}$

$\tan (60) = \dfrac{\text{H}}{16\sqrt{3}}}$

$H = \dfrac{16\sqrt{3} }{\tan(60)}$

$H = 48 \text{ units}$

Find the height of the cloud:

$\text{Height of the cloud} = 16 + 48$

$\text{Height of the cloud} = 64 \text {units}$

Answer: The cloud is 64 units high from the building.