The angle of elevation of the top of a tower from a tower from a point on the ground ,which is 30 away from the foot of the tower ,is 30 . Find height of the tower
Answers
Let the height of the tower be h
The distance between the tower and the angel of elevation is 30
Tan30= h/30
1/√3=h/30
h=10√3
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 :
$$\begin{lgathered}\sf\implies \tan30\degree = \dfrac{x}{150m} \\\\ \sf\implies \dfrac{1}{\sqrt{3}}=\dfrac{x}{150m}\\\\ \sf\implies x = \dfrac{150m}{\sqrt{3}} \\\\ \sf\implies x = 50\sqrt{3} m \\\\ \sf\implies x = 86.5m\end{lgathered}$$