Aptitude · all questions

Height And Distance
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Q101

Open question

The length of the shadow of a vertical tower on level ground increased by 10 m when the altitude of the sum changes from 45° to 30°. The height of the tower is:

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Q102

Open question

The respective ratio between the height of tower and the point at some distance from its foot is 57 : 19√3. What is the angle (in degrees) of elevation of the top of the tower?

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Q103

Open question

A balloon leaves from a point P rises at a uniform speed. After 6 minutes, an observer situated at a distance of 450√3 meter from point P observes that angle of elevation of the balloon is 60°. Assume that point of observation and point P are on the same level. What is the speed (in m/s) of the balloon?

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Q104

Open question

A ladder is placed against a wall such that it just reaches the top of the wall. The foot of the ladder is at a distance of 5 metres from the wall. The angle of elevation of the top of the wall from the base of the ladder is 15°. What is the length (in metres) of the ladder?

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Q105

Open question

Let A and B be two towers with the same base. From the mid point of the line joining their feet, the angles of elevation of the tops of A and B are 30° and 45° respectively. The ratio of the heights of A and B is:

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Q106

Open question

From the top of 75 m high tower, the angle of depression of two points P and Q on opposite side of the base of the tower on level ground is

θ

and

ϕ

, such that

tan θ = \frac{3}{4}

and

tan ϕ = \frac{5}{8} .

What is the distance between the points P and Q?

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Q107

Open question

A ladder leaning against a wall makes an angle

θ

with the horizontal ground such that

tan θ = \frac{12}{5} .

If the height of the top of the ladder from the wall is 24 m, then what is the distance (in m) of the food the ladder from the wall?

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Q108

Open question

A vertical pole and a vertical tower are on the same level ground in such a way that, from the top of the pole, the angle of elevation of the top of the tower is 60° and the angle of depression of the bottom of the tower is 30°. If the height of the pole is 24 m, then find the height of the tower (in m).

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Q109

Open question

A pole 23 m long reaches a window which is

35 m

above the ground on one side of a street. Keeping its foot at the same point, the pole is turned to the other side of the street to reach a window

415 m

high. What is the width (in m) of the street?

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Q110

Open question

Exactly midway between the foot of two towers P and Q, the angles of elevation of their tops are 45° and 60°, respectively. The ratio of the heights of P and Q is:

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Q111

Open question

The length of the shadow of a vertical pole on the ground is 36 m. If the angle of elevation of the sun at that time is

θ

such that

sec θ = \frac{13}{12},

then what is the height (in cm) of the pole?

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Height And Distancepractice.

Height And Distance
practice.