The ratio of the height of a tower and the length of its shadow on the ground is √3:1. What is the angle of elevation of the sun?

Solution

Let the height of the tower be x and y the length of the shadow on the ground be x:y.

The angle of elevation of the sun from the ground is θ.
We have, x:y =√3:1
Now, In ∆ABC
$tan space straight theta space equals fraction numerator space Height space over denominator Base end fraction tan space straight theta space equals space AB over BC space tan space straight theta space equals fraction numerator square root of 3 over denominator 1 end fraction therefore space tan space straight theta space space equals space 60 degree$

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Some Applications Of Trigonometry

The ratio of the height of a tower and the length of its shadow on the ground is √3:1. What is the angle of elevation of the sun?

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