# Applications of Trigonometry

Applications(uses) of trigonometry are in various fields:-

*Trigonometry is used to find the height of any object.**To find the distance between any object A to object B.**Height of statue if it is placed on some height.**There are other different fields.........*

*For better understanding, you should read our article on trigonometry.*

## 1. How to use trigonometry to find the height?

To find the height of any object we need to understand it with the help of an example:-

**Find the height of a tower which is situated 20m away from a building. An angle of 30Âº from the foot of building to the top of the tower.**

Solve:-

All details are shown in the below picture:-

*Angle(Î¸)=30Âº*

*CB(Base) = 20m*

*We need to find the height of tower AB(Perpendicular) =?*

We know that

*tanÎ¸ = (Perpendicular / Base)*......Eq.1Put all the values in Eq.1

tan30Âº = AB/CB

1/√3 = AB / 20

*{Value of tan30Âº = 1/√3}*20√3 = AB

So the height of tower AB is 20√3 m.

{We may put the value of √3 = 1.73 & solve it}

## 2. How to use trigonometry to find the distance between objects?

To find the distance between the object we need an example. Let's discuss-

**Find the distance between an object & building. If the height of the building is 10m & object makes an angle of 45Âº to the top of the building.**

Solve:-

All details are shown in the below picture:-

*Angle(Î¸)=45Âº*

*AB(Perpendicular) = 10m*

*We need to find the distance between an object to building CB(Base)=?*

We know that

*tanÎ¸ = (Perpendicular / Base)*......Eq.1Put all the values in Eq.1

tan45Âº = AB/CB

1 = 10 / CB

*{Value of tan45Âº = 1}*1×CB = 10

CB = 10

So the distance between object to building CB is 10 m.