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Height and Distance
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Height and Distance
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From a point P on a level ground, the angle of elevation of the top tower is 30º. If the tower is 100 m high, the distance of point P from the foot of the tower is
A. 148m
B. 162m
C. 164m
D. 173m
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If the angle of elevation of cloud from a point 200 m above a lake is 30º and the angle of depression of its reflection in the lake is 60º, then find the height of the cloud above the lake.
A. 400m
B. 600m
C. 800m
D. 1000m
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If the elevation of the sun changed from 30º to 60º, then find the difference between the lengths of shadows of a pole 15 m high, made at these two positions.
A. 4√3 m
B. 7√3 m
C. 10√3 m
D. 13√3 m
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The altitude of the sun at any instant is 60º. Find the height of the vertical pole that will cast a shadow of 30 m.
A. 10√3 m
B. 20√3 m
C. 30√3 m
D. 40√3 m
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From the top of a cliff 25 m high the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. Find the height of the tower.
A. 20 m
B. 50m
C. 130m
D. 170m
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A vertical tower stands on a horizontal plane and is surmounted by a flagstaff of height 7m. At a point on the plane, the angle of elevation of the bottom of the flagstaff is 30º and that of the top o
A. 9.562 m
B. 19.562 m
C. 29.562 m
D. 39.562 m
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A balloon is connected to a meteorological station by a cable of length 200 m, inclined at 60º to the horizontal. Find the height of the balloon from the ground. Assume that there is no slack in the c
A. 152.9 m
B. 164.6 m
C. 173.2 m
D. 188.4 m
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A ladder against a vertical wall makes an angle of 45º with the ground. The foot of the ladder is 3m from the wall. Find the length of the ladder.
A. 2.23 m
B. 4.23 m
C. 6.23 m
D. 8.23 m
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The shadow of a building is 20 m long when the angle of elevation of the sun is 60º. Find the height of the building.
A. 34.64 m
B. 38.64 m
C. 42.64 m
D. 49.64 m
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From the top of a temple near a river the angles of depression of both the banks of river are 45° & 30°. If the height of the temple is 100 m then find out the width of the river.
A. 50(√3-1)m
B. 100(√3-1)m
C. 200(√3-1)m
D. 300(√3-1)m
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The angle of elevation of the top of a tower from a point on the ground is 30° . On walking 100m towards the tower the angle of elevation changes to 60° . Find the height of the tower.
A. 80√3
B. 70√3
C. 60√3
D. 50√3
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The thread of a kite is 120 m long and it is making 30° angular elevation with the ground .What is the height of the kite?
A. 60m
B. 40m
C. 20m
D. 10m
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Two vertical poles are 200 m apart and the height of one is double that of the other. From the middle point of the line joining their feet, an observer finds the angular elevations of their tops to be
A. 90.5 m and 121 m
B. 80.5 m and 131 m
C. 70.5 m and 141 m
D. 60.5 m and 151 m
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The angles of depression and elevation of the top of a wall 11 m high from top and bottom of a tree are 60° and 30° respectively. What is the height of the tree?
A. 11m
B. 22m
C. 33m
D. 44m
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A vertical tower stands on ground and is surmounted by a vertical flagpole of height 18 m. At a point on the ground, the angle of elevation of the bottom and the top of the flagpole are 30° and 60° re
A. 9m
B. 4m
C. 12m
D. 8m
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The angle of elevation of the top of a lighthouse 60 m high, from two points on the ground on its opposite sides are 45° and 60°. What is the distance between these two points?
A. 104.6 m
B. 94.6 m
C. 84.6 m
D. 74.6 m
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A ladder 10 m long just reaches the top of a wall and makes an angle of 60° with the wall.Find the distance of the foot of the ladder from the wall ( √ 3 = 1.73 )
A. 8.65 m
B. 10.65 m
C. 12.65 m
D. 14.65 m
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A person, standing exactly midway between two towers, observes the top of the two towers at angle of elevation of 22.5° and 67.5°. What is the ratio ? (Given that tan 22.5° = √ 2 − 1 )
A. 7+2√2: 1
B. 1+2√2: 1
C. 5+2√2: 1
D. 3+2√2: 1
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Find the angle of elevation of the sun when the shadow of a pole of 18 m height is 6 √ 3 m long?
A. 60°
B. 70°
C. 80°
D. None of these
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The elevation of the summit of a mountain from its foot is 45°. After ascending 2 km towards the mountain upon an incline of 30°,the elevation changes to 60°. What is the approximate height of the mou
A. 12.7 km
B. 22.7 km
C. 2.7 km
D. 32.7 km
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