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Question
The length of the shadow of a tower on the plane ground is `sqrt(3)` times the height of the tower. Find the angle of elevation of the sun.
Sum
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Solution
Given: Let the tower's height = h and the shadow's length = `sqrt(3) xx h`.
In the right triangle formed by tower and its shadow.
`tan θ = "height"/"shadow"`
= `h/(sqrt(3) xx h)`
= `1/sqrt(3)`
= `sqrt(3)/3`
Hence `θ = arctan(1/sqrt(3))` = 30°.
The angle of elevation of the sun is 30°.
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