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At the foot of a mountain the elevation of its peak is found t

Question

At the foot of a mountain the elevation of its peak is found to be $\frac{π}{4} .$ After ascending $h$ metres toward the mountain up a slope of $\frac{π}{6}$ inclination, the elevation is found to be $\frac{π}{3} .$ Height of the mountain is

\frac{h}{2} (3 + 1) m

h (3 + 1) m

\frac{h}{2} (3 - 1) m

h (3 - 1) m

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Elijah Discussed

At the foot of a mountain the elevation of its peak is found to be

\frac{π}{4} .

After ascending

h

metres toward the mountain up a slope of

\frac{π}{6}

inclination, the elevation is found to be

\frac{π}{3} .

Height of the mountain is

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

Let 'A' be the top of hill and 'P' be a point on it's foot.
We have

∠ A PB = \frac{π}{4}, ∠ QPB = \frac{π}{6}, ∠ A QR = \frac{π}{3}, PQ = h m

Δ A PB,

PB = A B cot \frac{π}{4} = A B

Δ P Q_{1} Q

Q Q_{1} = PQ sin \frac{π}{6} = \frac{h 3}{2}

Δ A QR, tan \frac{π}{3} = \frac{A R}{QR} = \frac{A B - Q Q _{1}}{PB - P Q _{1}}

\Rightarrow \frac{A B - \frac{h}{2}}{A B - \frac{h 3}{2}} = 3

\Rightarrow A B = \frac{h}{( 3 - 1 )} = \frac{h ( 3 + 1 )}{2} m

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Question Text	At the foot of a mountain the elevation of its peak is found to be $\frac{π}{4} .$ After ascending $h$ metres toward the mountain up a slope of $\frac{π}{6}$ inclination, the elevation is found to be $\frac{π}{3} .$ Height of the mountain is
Answer Type	Text solution:1
Upvotes	150