A man is walking towards a vertical pillar in a straight path at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 30 o . After walking for 5 3 + 1 minutes from A in the same direction, at a point B , he observes that the angle of elevation of the top of the pillar is 45 o . Then the time taken (in minutes) by him, to reach from B to the pillar, is (take 3 = 1 .73 )

Question

A man is walking towards a vertical pillar in a straight path at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 30 o . After walking for 5 3 + 1 minutes from A in the same direction, at a point B , he observes that the angle of elevation of the top of the pillar is 45 o . Then the time taken (in minutes) by him, to reach from B to the pillar, is (take 3 = 1 .73 ),

MARKS App · Accepted Answer

In ∆ Q P A : h x + y = tan ⁡ 30 o ⇒ 3 h = x + y … ….(i) In ∆ Q P B : h y = tan ⁡ 45 o ⇒ h = y … … .(ii) From (i) and (ii), we get, 3 y = x + y ⇒ y = x 3 − 1 Given that the distance x is covered in 5 3 + 1 minutes Hence, the distance x 3 − 1 is covered in 5 3 + 1 3 − 1 = 5 2 + 3 = 18 . 65 minutes

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