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### Trigonometry - Quant/Math - CAT 2016

Question 4 the day: March 25, 2005

The question for the day is a quant problem on heights and distances using trigonometric concepts.

Question:
A spherical ball of radius 'r' placed on the ground subtends an angle of 600 at point A of the ground. What is the distance between the center of the ball and the point A?
(1) r
(2) 2r
(3) 0.5r
(4) none of these
Correct choice (2). Correct Answer - (2r)

Solution:

In an equilateral triangle all three sides are of the same length and let this be 'a' units.

From the diagram it is clear that OA is the angle bisector of angle LAM.

Therefore, angle OAL = 30
In the right triangle OAL, sin 30 =
We know that OL is the radius of the sphere = r
Therefore,
Or OA = 2r

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