Application of trigonometric ratio

Line of Sight: it is the line joining eye of observer to the point in the object.

The angle of Elevation: It is angle made by line of sight with the horizontal

when object viewed is above the horizontal.

The angle of depression:It is angle made by line of sight with the horizontal

when object viewed is below the horizontal.

E.g.: A peacock seesa cloud at the angle of $\text{30°}$. The cloud is at certain height from the ground. If the horizontal distance from peacock to the point from where the height of cloud is measured is $\text{100}$ m.Find the height of cloud.

Suppose $\text{A -}$ cloud

$\text{C =}$ peacock

$\text{B =}$ is point from where the height of cloud is measured.

$\angle \text{ACB = 30°}$

BC $\text{= 100}$ m

To find: $\text{AB}$.

$\text{Tan C = }\frac{\text{opposite side to C}}{\text{Adjacent side to A}}$

$\text{Tan 30 = }\frac{\text{AB}}{\text{BC}}$

$\frac{1}{\sqrt{3}}\text{ = }\frac{\text{AB}}{\text{100}}$

$\frac{100}{\sqrt{3}}\text{ = AB}$

$\frac{\text{100}\sqrt{\text{3}}}{\text{3}}\text{ = AB}$

$\therefore \text{AB = }\frac{\text{100}\sqrt{\text{3}}}{\text{3}}\text{m}$