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If two towers of height x and y subtend angles of 30 degree and 60 degree respectively at the centre of a line joining their feet then find the ratio of x and y
  • a)
    1 : 3
  • b)
    1 : 1
  • c)
    3 : 1
  • d)
    1 : 2
Correct answer is option 'A'. Can you explain this answer?
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If two towers of height x and y subtend angles of 30 degree and 60 deg...
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If two towers of height x and y subtend angles of 30 degree and 60 deg...
Given:
- Two towers of height x and y
- They subtend angles of 30 degree and 60 degree respectively at the centre of a line joining their feet

To find: Ratio of x and y

Solution:

Let O be the center of the line joining the feet of the towers.

Let A and B be the tops of the two towers.

OA = OB = r (say)

In triangle OAB,

angle AOB = 60 degree

angle OAB = 30 degree

angle OBA = 90 degree

Applying trigonometry,

- In triangle OAB,

tan 30 degree = x / r

tan 60 degree = y / r

- Dividing the above two equations, we get,

tan 30 degree / tan 60 degree = x / y

1 / √3 = x / y

x/y = √3

Therefore, the ratio of x and y is 1:3.

Hence, option A is the correct answer.
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