Question
Download Solution PDFFind the angle of elevation of the sun when the length of the shadow of a pole is equal to the height of the pole.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The length of the shadow of a pole is equal to the height of the pole.
Concept:
The angle of elevation of the sun creates a right-angled triangle where the height of the pole (opposite side) is equal to the length of the shadow (adjacent side).
Formula Used:
In a right-angled triangle, when the opposite side is equal to the adjacent side, the angle of elevation (θ) can be found using the tangent function:
tan(θ) = opposite / adjacent
Since opposite = adjacent, we have:
tan(θ) = 1
Calculation:
We need to find θ such that:
⇒ tan(θ) = 1
From trigonometric tables or knowledge, we know:
⇒ θ = 45º
∴ The angle of elevation of the sun is 45º.
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