Subject - Mathematics:

Height and Distance

MCQ - 466-9198

Question:

If the height of a vertical pole is v3 times the length of its shadow on the ground then the angle of elevation of the sun at that time is

30°
45°
60°
45°

Correct Answer: C

Explanation:

Let AB be the pole and BC be the shadow. Join A and C. We get a right-angled triangle right angled at B. The angle of elevation of the sun is ∠ ACB (= θ, say). We use the trigonometric ratio tan for the triangle taking AB as height and BC as the base. By the problem, AB = √3BC.
In ∆ABC,
tanθ = $\frac{AB}{BC}$ = $\frac{√3BC}{BC} √3$
or,
θ = 60°
since we know that tanθ is √3 whenever θ = 60°.

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