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MathematicsHard
Trigonometry
Heights And Distances

The angle of elevation of a cloud from a point h meters above a lake is α and the angle of depression of its reflection is β. The height of the cloud is:

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MathematicsHard
Trigonometry
Heights And Distances

A man on the deck of a ship 10 m above water level observes elevation of a hill top as 60° and depression of base as 30°. Find hill height.

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MathematicsHard
Trigonometry
Heights And Distances

A round balloon of radius r subtends an angle θ at the eye of an observer, while the angle of elevation of its center is φ. Height of center?

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MathematicsHard
Trigonometry
Heights And Distances

A ladder rests against a wall at α to the horizontal. Its foot is pulled a distance 'a' away so it slides 'b' down the wall, making angle β. Find a/b.

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MathematicsHard
Trigonometry
Heights And Distances

Angle of elevation of top of a tower from point A is 30°. From point B, 20 m closer, it is 60°. Find tower height.

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MathematicsHard
Trigonometry
Heights And Distances

A vertical tower is surmounted by a flagstaff of height h. At a point on ground, elevations of bottom and top of flagstaff are α and β. Tower height is:

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MathematicsHard
Trigonometry
Heights And Distances

From a point on ground, the elevation of a tower is θ. After walking a distance 'a' towards it, elevation is 45°, and after 'b' more, it is 90-θ. Height is:

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MathematicsHard
Trigonometry
Heights And Distances

An aeroplane at altitude h observes two points on opposite sides of the river at angles α and β. Width of river?

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MathematicsHard
Trigonometry
Heights And Distances

The angle of elevation of a stationary helicopter from a point is 60°. After rising 100 m vertically, the angle of depression of the point is 45°. Find the original height.

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MathematicsHard
Trigonometry
Heights And Distances

If a pole of height h is at the center of a square of side 'a', and θ is elevation of its top from a corner, then:

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MathematicsHard
Trigonometry
Heights And Distances

A ladder rests against a vertical wall at angle α. If its foot is pulled distance 'a' so it makes angle β, the distance 'b' it slides down is:

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MathematicsHard
Trigonometry
Heights And Distances

A tower subtends an angle α at a point A and elevation of top of a flagstaff on it is β. If h is flagstaff height, tower height is:

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MathematicsHard
Trigonometry
Heights And Distances

Shadow of tower is 30m when elevation is 30°. When elevation is 60°, shadow is:

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MathematicsHard
Trigonometry
Heights And Distances

From top of tower h, elevation of a balloon is α and depression of its reflection is β. Height of balloon?

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MathematicsHard
Trigonometry
Heights And Distances

Angle of elevation of top of tower from a point A is α. Walking distance 'd' towards it, it is β. Height h is:

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MathematicsHard
Trigonometry
Heights And Distances

A flagstaff on a tower 20 m high subtends 45° at a point 20 m from the foot. Flagstaff height?

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MathematicsHard
Trigonometry
Heights And Distances

Angle of elevation of an object from a point 100 m high is 30°. If the object is 200 m from the base, find its height.

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MathematicsHard
Trigonometry
Heights And Distances

If the elevation of sun changes from 30 to 60, the shadow of a tower decreases by 10 m. Height?

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MathematicsHard
Trigonometry
Heights And Distances

Height of two towers are h1 and h2. If elevation of top of first from foot of second is 60 and vice versa is 30, h1/h2 is:

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MathematicsHard
Trigonometry
Heights And Distances

A man in a boat moving away from a cliff 100 m high takes 2 mins for elevation to change from 60 to 30. Speed?

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