Math, asked by Anonymous, 5 months ago

The angle of elevation of the top of a tower from a point 15 meters away from the

base is 30.Find the height of the tower. Explain​

Answers

Answered by MaheswariS
1

\underline{\textbf{Given:}}

\textsf{The angle of elevation of the top of a tower from a point}

\textsf{15m away from the base is}\;\mathsf{30^\circ}

\underline{\textbf{To find:}}

\textsf{Height of the tower}

\underline{\textbf{Solution:}}

\textsf{Let C be the point of obserrvation and AB be the tower}

\mathsf{In\;\triangle\;ABC,}

\mathsf{tan\,30^\circ=\dfrac{Opposite\;side}{Adjacent\;side}}

\mathsf{tan\,30^\circ=\dfrac{AB}{BC}}

\mathsf{\dfrac{1}{\sqrt3}=\dfrac{AB}{15}}

\mathsf{AB=\dfrac{15}{\sqrt3}}

\mathsf{AB=\dfrac{5{\times}3}{\sqrt3}}

\implies\mathsf{AB=5\sqrt3}

\implies\mathsf{AB=5{\times}1.732}

\implies\boxed{\mathsf{AB=8.66\;m}}

\therefore\textsf{Height of the tower is 8.66 m}

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Answered by Anonymous
0

Given - Angle of elevation - 30°

Distance from tower - 15 metres.

Find - Height of the tower.

Solution - The tower and the line joining angle of elevation at 15 metre distance will form a right angled triangle.

Let the height of tower be AB, Distance from tower BC and hence, the line joining the angle to the top of tower will be AC. Angle C is 30°.

Therefore, tan 30° = perpendicular/base

tan 30° = AB/15

AB = 15/✓3

AB = 15/1.732

AB = 8.6 metre.

Hence, the height of tower is 8.6 metre.

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