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The shadow of a tower is 30 meters when the sun's altitude is 30∘. When the sun's altitude is 60 $°$ then the length of shadow will be [[1]].

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Detailed Solution

In fig. AB is the tower , BC is the length of the shadow of tower when altitude is 30

°

i.e the angle of elevation of the top of the tower from the tip of the shadow is 30

°

and DB is the length of the shadow, when the angle of elevation is 60

°

Given, BC = 30 m
In triangleABC,
Tan30

° = \frac{AB}{BC}

Or,

\frac{1}{\sqrt{3}} = \frac{AB}{30}

Or, AB=

\frac{30}{\sqrt{3}} = 10 \sqrt{3}

m
Again, In triangle ABD,
Tan60

° = \frac{AB}{BD}

Or,

\sqrt{3} = \frac{10 \sqrt{3}}{BD}

Or, BD = 10m

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