Indian Institute of Foreign Trade 2017 Solved Paper

Question : 67 of 114

Marks: +1, -0

A flag pole on the top of a mall building is 75 m high. The height of the mall building is 325 m. To an observer at a height of 400 m, the mall building and the pole subtend equal angle 0. If the horizontal distance of the observer from the pole is 'x', then what is the value of X?

$20√10$
$30√10$
$25√5$
None

Validate

Solution:

Choice (B) The flag pole and mall buildings are shown in the following diagram.

Since SQ is the angle bisector, hence

{ \SR }/ { \SP } = { 75 } /{ 325 } = { 3 }/ { 13 }

Now

\ST ^ { 2 } = ( 13 k ) ^ { 2 } - ( 3 k ) ^ { 2 }

⇒160 k ^ { 2 } = 400 ^ { 2 }

k = { 100 } /{ √ { 10 } } = 10 √ { 10 }

Hence PT =

3k = 30√ 10

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