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A train travelling on one of two interse...

A train travelling on one of two intersecting railway lines, subtends at a certain station on the other line, an angle `alpha` when the front of the carriage reaches the junction, and an angle `beta` when the end of the carriage reaches it. Prove that the two lines are inclined to each other at an angle `theta` determined by `2cot theta = cot alpha - cot beta`.

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The correct Answer is:
`2 cot theta = cot alpha - cot beta`
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FIITJEE-HEIGHTS & DISTANCE -ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-II
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  2. The height of a house subtends a right angle at the opposite street li...

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  3. The angle of elevation of the top of a tower at a point A due south of...

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  4. The angle of elevation of a tower PQ at a point A due north of it is 3...

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  5. An electric pole stands at the vertex A of the equilateral triangular ...

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  6. A pole on the ground lenses 60^(@) to the vertical. At a point a meter...

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  7. A 10 meters high tower is standing at the centre of an equilateral tri...

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  8. A tower subtends an angle alpha at a point A in the plane of its base ...

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  9. A tower subtends angle theta, 2theta, 3theta at the three points A,B a...

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  10. A spherical balloon of radius 50 cm, subtends an angle of 60^(@) at a ...

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  11. PQ is a post of height a, AB is a tower of height h at a distance x fr...

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  13. The base of a cliff is circular. From the extremities of a diameter of...

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  14. A round balloon of radius r subtends an angle alpha at the eye of the ...

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  15. .A house of height 100 m substends a right angle at the window of an o...

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  16. A tower subtends an angle alpha at a point A in the plane of its...

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  17. ABCD is a rectangular field. A vertical lamp post of height 12 m stand...

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  18. A tower of x metres height has flag staff at its top. The tower and th...

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  19. An aeroplane flying horizontally , 1km above the ground , is observed...

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  20. A man in a boat rowed away from a cliff 150 m high takes 2 min, to cha...

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  21. The angle of elevation of the cloud at a point 2500 m high from the la...

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