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Question
At some time of the day, the length of the shadow of a tower is equal to its height. Then, the sun’s altitude at that time is ______.
Options
30°
60°
90°
45°
Solution
At some time of the day, the length of the shadow of a tower is equal to its height. Then, the sun’s altitude at that time is 45°.
Explanation:
Let the height of tower BC = x m and the sun’s altitude = θ
Then Length of its shadow, AB = x m
In right-angled ΔABC, tan θ = `"BC"/"AB" = "x"/"x"` = 1
⇒ tan θ = tan 45°
θ = 45°
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