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The length of the shadow of a tower is 9...

The length of the shadow of a tower is 9 metres when the sun's angle of elevation is `30^(@)`. Calculate the height of the tower.

Text Solution

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Let AB be the tower and BC be its shadow.
As per question, BC = 9 m and `angleACB = 30^(@)`.
Now, from the right-angled triangle ABC we get,
`tan 30^(@) = (AB)/(BC)` [ by definition]
or, `(1)/(sqrt(3)) = (AB)/(9)`
or, `sqrt(3)AB = 9`
or, AB = `(9)/(sqrt(3)) = 3sqrt(3)`
Hence the height of the tower = `3sqrt(3)` metres.
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