Math-Applications-Of-Trigonometry-Questions

Class: X
Subject:
√ Math’s
Topic: Some Applications of trigonometry
No. of Questions: 20
Q.1 The angle of elevation of the top of a tower from a point on the ground, which is 30
m away from the foot of the tower, is 300. Find the height of the tower.
Q.2 A kite is flying at a height of 60 m above the ground. The string attached to the kite
is temporarily tied to a point on the ground. The inclination of the string with the
ground is 600. Find the length of the string assuming that there is no slack in the
string.
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Q.3 A circus artist is climbing from the ground along a rope stretched from the top of a
vertical pole and tied at the ground. The height of the pole is 12 m and the angle
made by the rope with ground level is 300. Calculate the distance covered by the
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artist in climbing to the top of the pole.
A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from
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the top of a vertical pole to the ground. Find the height of the pole if the angle made
by the rope with the ground level is 300.
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Q.5 A bridge across a river makes an angle of 45o with the river bank as shown in the
figure. If the length of the bridge across is 150m, what is the width of the river?
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Q.6 An observer 1.5m tall is 28.5m away from a tower. The angle of elevation of the top
of the tower her eyes is 45o. What is the height of the tower?
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Q.7 A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-
staff of height h. At a point on the plane, the angles of elevation of the bottom and
the top of the flag-staff are α and β respectively. Prove that the height of the tower is
(h tan α) / (tan β – tan α)
Q.8 A tree is broken by the wind. The top struck the ground at an angle of 30o and at a
distance of 30 metres from the root. Find the whole height of the tree.
Q .9 The angles of elevation of the top of a tower from two points at distances a and b
metres from the base and in the same straight line with it are complimentary. Prove
that the height of the tower is ab metres. (CBSE-2004)
Q .10 At a point on level ground, the angles of elevation of a vertical tower are found to be
such that its tangent is 5 / 12. On waling 192 metres towards the tower, the tangent
of the angle of elevation is 3 / 4. Find the height of the tower.
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Q .11 The shadow of a vertical tower on level ground increases by 10 metres, when the
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altitude of the sun changes from angle of elevation 45o and 30o. Find the height of
the tower, correct to one place of decimal. (Take 3 = 1.73)
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Q .12 From the top of a hill, the angles of depression of two consecutive kilometer stones
due east are found to be 30o and 45o. Find the height of the hill.
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Q .13 An aeroplane at an altitude of 1200 metres finds that two slips are sailing towards it
in the same direction. The angles of depression of the ships as observed from the
aeroplane are 60o and 30o respectively. Find the distance between the two ships.
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Q.14 The shadow of a flag staff is three times as long as the shadow of the flag staff when
the sun rays meet the ground at an angle of 600. Find the angle between the sun rays
and the ground at the time of longer shadow.
Q.15 An airplane at an altitude of 200 metres observes the angles of depression of

opposite points on the two banks of a river to be 45o and 60o. Find the width of the
river.
Q .16 As observed from the top of a light house, 100m above sea level, the angle of
depression of a ship, sailing directly towards it, changes from 30o to 45o. Determine
the distance travelled by the ship during the period of observation. (CBSE-2004)
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Q.17 From the top of a building 60m high the angles of depression of the top and the
bottom of a tower are observed to be 30o and 60o. Find the height of the tower.
(CBSE-2005)
Q.18 The angles of elevation of a cloud from a point 60m above a lake is 30o and the angle
of depression of the reflection of cloud in the lake is 60o. Find the height of the cloud.
Q.19 The horizontal distance between two towers is 140m. The angle of elevation of the
top of the first tower when seen from the top of the second tower is 30o. If the height
of the second tower is 60m, find the height of the first tower.
Q.20 An aeroplane when flying at a height of 4000 m from the ground passes vertically
above another aeroplane at an instant when the angles the angles of the elevation of
two planes from the same point on the ground are 600 and 450 respectively. Find the
vertical distance between them at that instant.
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(CBSE-2009)
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Class: X

Q.15 An airplane at an altitude of 200 metres observes the angles of depression of

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