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  • A ladder 15 metres long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, find the height of the wall.

A ladder 15 metres long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, find the height of the wall.

Answers (1)

Length of ladder = 15 m
The angle between wall and ladder = 60°
Let the height of wall = H

In \bigtriangleupABC  \angleC = 60°, \angleB = 90°
We know that
\angleA + \angleB + \angleC = 180°   (Sum of interior angles of a triangle is 180)
\angleA + 90 + 60 = 180°
\angleA = 30°
In \bigtriangleupABC      

\sin 30^{\circ} = \frac{H}{15}
H= \sin 30^{\circ} \times 15
H= \frac{1}{2} \times 15        \left ( \because \sin 30^{\circ} = \frac{1}{2}\right )
H= 7\cdot 5\, m
Hence the height of the wall is 7.5 m

 

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infoexpert27

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