Question

the angle of elevation from the top of the tower from a point on a ground which is 30 metres from the foot of the tower is 30° find the height of Tower

Answer 1

hope it will be helpful to you

Answer 2

Answer

The height of the tower is 86.5m

\bf\large\underline{Given}

Given

The angle of elevation of a tower , from a point on the ground and at a distance of 150m from its foot, is 30°

\bf\large\underline{To \: Find}

ToFind

The height of the tower

\bf\large\underline{Solution}

Solution

Let us consider the height of the tower be x m

From ‘tan’ function we have :

\sf\bullet \: \: \tan\theta =\dfrac{height}{base}∙tanθ=

base

height

Applying trigonometric ‘tan’ on the given data :

$$\begin{lgathered}\sf\implies \tan30\degree = \dfrac{x}{150m} \\\\ \sf\implies \dfrac{1}{\sqrt{3}}=\dfrac{x}{150m}\\\\ \sf\implies x = \dfrac{150m}{\sqrt{3}} \\\\ \sf\implies x = 50\sqrt{3} m \\\\ \sf\implies x = 86.5m\end{lgathered}$$

Thus , height of the tower correct to one place of decimal is 86.5m