Question

How do you find height with angle and distance?

Answer 1

Find height with angle and distance : The height of an object is obtained by measuring the distance from the object and the angle of elevation of the top of the object. The tangent of the angle is the object height divided by the distance from the object. Thus, the height is found.

The angle of elevation: The angle between the horizontal and the line of sight joining an observation point to an elevated object.

For example :

Suppose angle of elevation from a point A to the top of the tower is ${45}^0$.and distance from a point A to the bottom of the tower is $10$meter.

$\angle BAC={45}^0,AC=10$meter

Now, we need to find height of the tower i.e. $BC$.

$$\begin{gathered} \tan {45}^0=\frac{BC}{AC} \\ \Rightarrow 1=\frac{BC}{10} \\ \Rightarrow BC=10 \end{gathered}$$

Therefore the height of the tower is $10$meter.