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The angle of elevation of the top of the tower from the point $a$ meter away from the base of the tower is $60 °$ . The height of the tower is ____ meter.

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Detailed Solution

The angle of elevation of the top of the tower from the point

a

meter away from the base of the tower is

60 °

.The height of the tower is

\sqrt{3} a

meter.
It is given that the angle of elevation of the top of the tower from the point

a

meter away from the base of the tower is

60 °

.
According to the given data the figure has been drawn below.
Question Image

Let

AB

be the height of the tower.
The angle of elevation of the top of the tower from the point

a

meter away from the base of the tower is

60 °

∴ BC = a

meter and

∠ ACB = 60 °

.
In

△ ABC,

tan θ = P e r p e n d i c u l a r b a s e

\tan 60 ° = \frac{AB}{BC}

\Rightarrow \sqrt{3} = \frac{AB}{a}

∵ tan 60 ° = 3

\Rightarrow AB = \sqrt{3} a

∴

The height of the tower is

\sqrt{3} a

meter.
So answer is

\sqrt{3} a

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The angle of elevation of the top of the tower from the point a meter away from the base of the tower is 60°. The height of the tower is ____ meter.

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The angle of elevation of the top of the tower from the point $a$ meter away from the base of the tower is $60 °$ . The height of the tower is ____ meter.