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∘ . After walking for 10 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 60∘ . Then the time taken (in minutes) by him, from B to reach the pillar is:

tan60o=yb=3tan30o=x+ybtan30o=31Take t1=10 minx+y=b3As x=10p p be the speed10p+pt=3y3 (Put y=pt,x=10p,b=3y)⇒10p+pt=3pt⇒10+t=3t⇒10=2tt=5

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A man is walking towards a vertical pillar in a straight path,

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 $30^{\circ}$ . After walking for $10$ 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 $60^{\circ}$ . Then the time taken (in minutes) by him, from $B$ to reach the pillar is:

6

10

20

5

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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^{\circ}

. After walking for

10

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

60^{\circ}

. Then the time taken (in minutes) by him, from

B

to reach the pillar is:

6 mins ago

Discuss this question LIVE

6 mins ago

tan 6 0^{o} = \frac{b}{y} = 3

tan 3 0^{o} = \frac{b}{x + y}

tan 3 0^{o} = \frac{1}{3}

Take

t_{1} = 10

min

x + y = b 3

x = 10 p

p

be the speed

10 p + pt = 3 y 3

(Put

y = pt, x = 10 p, b = 3 y

)

\Rightarrow 10 p + pt = 3 pt

\Rightarrow 10 + t = 3 t

\Rightarrow 10 = 2 t

t = 5

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Question Text	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 $30^{\circ}$ . After walking for $10$ 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 $60^{\circ}$ . Then the time taken (in minutes) by him, from $B$ to reach the pillar is:
Answer Type	Text solution:1
Upvotes	150