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Question
The length of shadow of a tower on the plane ground is `sqrt3` times the height of the tower.
The angle of elevation of sun is:
Options
A. 45°
B. 30°
C. 60°
D. 90°
Solution
Let AB be the tower and BC be the length of the shadow of the tower.
Here, θ is the angle of elevation of the sun.
Given, length of shadow of tower = `sqrt3` × Height of the tower
BC = `sqrt3` AB ... (1)
In right ΔABC
`tanO/=(AB)/(BC)` `(tanO/=(\text{opposite side})/\text{opposite side})`
`thereforetanO/=(AB)/sqrt(AB)` `\text{Using} (1)`
`rArrtanO/=1/sqrt3`
`rArrtan=tan 30^@` `(thereforetan30^@=1/sqrt3)`
`rArrO/=30^@`
Thus, the angle of elevation of the sun is 30°.
Hence, the correct answer is B.
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