How to do the sum (the angle of elevation of the top of a tower, from a point on the ground and at distance of 150m, from its foot is 30 degree. find the height of the tower correct to one decimal place?
Answers
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