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An aeroplane when 3000 m high, passes vertically above another

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An aeroplane when $3000 m$ high, passes vertically above another aeroplane at an instant when the angles of elevation of the two aeroplanes from the same point on the ground are $6 0^{\circ}$ and $4 5^{\circ}$ respectively. Find the vertical distance between the two planes.

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An aeroplane when

3000 m

high, passes vertically above another aeroplane at an instant when the angles of elevation of the two aeroplanes from the same point on the ground are

6 0^{\circ}

and

4 5^{\circ}

respectively. Find the vertical distance between the two planes.

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Text solutionVerified

From

△ l e A, B, C

tan 6 0^{o} = \frac{3000}{BC}

BC = \frac{3000}{3} \times \frac{3}{3}

BC = 10003 m

tan (4 5^{o}) = \frac{A _{2} B}{BC} = \frac{A _{2} B}{1000 3}

A_{2} B = 10003 (1)

A, B - A_{2} B = 3000 - 10003

A_{1} A_{2} = 1000 (3 - 3) m

Vertical distance between

2

planes

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Question Text	An aeroplane when $3000 m$ high, passes vertically above another aeroplane at an instant when the angles of elevation of the two aeroplanes from the same point on the ground are $6 0^{\circ}$ and $4 5^{\circ}$ respectively. Find the vertical distance between the two planes.
Answer Type	Text solution:1
Upvotes	150

An aeroplane when 3000 m high, passes vertically above another aeroplane at an instant when the angles of elevation of the two aeroplanes from the same point on the ground are 60∘ and 45∘ respectively. Find the vertical distance between the two planes.

Text solutionVerified

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An aeroplane when $3000 m$ high, passes vertically above another aeroplane at an instant when the angles of elevation of the two aeroplanes from the same point on the ground are $6 0^{\circ}$ and $4 5^{\circ}$ respectively. Find the vertical distance between the two planes.