Quantitative Aptitude Quiz for SSC(Height and Distance): 31 March 2021

1. Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is

Source: safalta

a) 373m
b) 273m
c) 293m
d) 253m


2. A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30° with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60°. What is the distance between the base of the tower and the point P?

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a) 5.73 unit
b) 4 unit
c) 12 unit
d) Data Inadequate


3. The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is

a) 9.2m
b) 13.8 m
c) 2.3 m
d) 11.5m

4. An observer 1.6 m tall is 20√3 away from a tower. The angle of elevation from his eye to the top of the tower is 30°. The height of the tower is

a) 22.72 m
b) 21.6 m
c) 23.4 m
d) 20.98 m

5. From a point P on a level ground, the angle of elevation of the top tower is 30°. If the tower is 100 m high, the distance of point P from the foot of the tower is

a) 200m
b) 346m
c) 173m
d) 86.5 m

6. The angle of elevation of the sun, when the length of the shadow of a tree √3 times the height of the tree, is:

a) 30
b) 45
c) 60
d) 75



7.A man is standing on the deck of a ship, which is 10m above water level. He observes the angle of elevation of the top of a light house as 600 and the angle of depression of the base of lighthouse as 300. Find the height of the light house.
a) 30m
b) 40m
c) 45m
d) 38m



8. From the top of a building 60m high, the angle of elevation and depression of the top and the foot of another building are α and β respectively. Find the height of the second building.
a) 60(1+ tan α tanβ)
b) 60(1+ cot α tanβ)
c) 60(1+ tan α cotβ)
d) 60(1- tan αcotβ)



9. From the top of a tower 75m high, the angles of depression of the top and bottom of a pole standing on the same plane as the tower are observed to be 300 and 450 respectively. Find the height of the pole.
a) 30.4m
b) 35.9m
c) 28.6m
d) 31.7m


10. A 10 m long flagstaff is fixed on the top of a tower on the horizontal plane. From a point on the ground, the angles of elevation of the top and bottom of the flagstaff are 600 and 450 respectively. Find the height of the tower.
a) 5(√3 + 1)m
b) 5(√3 + 3)m
c) 10(√3 - 1)m
d) 10(√3 + 1)m