Answer :
Final answer:
The angle of elevation of the sun can be found using trigonometry by setting up a right triangle formed by the pole, the length of its shadow, and the angle of elevation. Using the tangent function, we can find the angle of elevation.
Explanation:
The angle of elevation of the sun when the shadow of a pole 'h' meters high is √3h meters long can be found using trigonometry. Let's assume that the angle of elevation is 'θ'. We have a right triangle formed by the pole, the length of its shadow, and the angle of elevation. The opposite side of the triangle is the height of the pole (h) and the hypotenuse is the length of the shadow (√3h). Using the tangent function, we can find the angle of elevation:
tan(θ) = h / (√3h) = 1 / √3 = 1 / √3 * √3 / √3 = √3 / 3
Now, we can use the inverse tangent function to find the angle of elevation:
θ = tan^(-1)(√3 / 3)
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