10th Application of Trigonometry Test Paper - 2

Class 10 Application of Trigonometry [Height and Distance] Test paper-02
1. The angle of elevation of a ladder leaning against a wall is 60 o and the foot of the ladder is
9.5 meter away from the wall. Find the length of the ladder.
Answer: 19m
2. If the length of the shadow cast by a pole be times the length of the pole, find the angle of
elevation of the sun.
Answer: 30o
3. A tree is broken by the wind. The top stuck the ground at an angle of 30 o and at a distance
of 30 m from the root. Find the total height of the tree.
4. A circus artist is climbing from the ground along a rope stretched from the top of vertical
pole and tied at the ground level 30o. Calculate the distance covered by the artist in climbing to
the top of the pole.
Answer: 24 m
5. A person standing on the bank of a river observes that the angle of elevation of the top of a
tree standing on the opposite bank is 60o. When he was 40 m away from the bank he finds that
the angle of elevation to be 30o. Find: (i) The height of the tee , (ii) The width of the river,
correct up to two decimal places.
Answer: (i) 34.64m (ii) 20m
6. An aeroplane when flying at a height of 4000 m from the ground passes vertically above
another aeroplane at an instant when the angles of elevations of two planes to a same point on
the ground are 60o and 45o respectively. Find the vertical distance between the areoplane at
that at that instant.
Answer: 1693.34 m
7. The angle of elevation of the top of the hill at the foot of a tower is 60o and the angle of
elevation of the top of tower from the foot of hill is 30o. If the tower is 50 m high, what is the
height of the hill..
Answer: 150 m
8. There is a small island in the middle of a 100 m wide river and a tall tree stands on the
island. Let P and Q be points directly opposite each other on the two banks, and in line with the
tree. If the angles of elevation of the top the tree from P and Q respectively are 30o and 45o,
find the height of the tree.
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9. Two pillars of equal heights are on either sides of a roadway, which is 150 m wide. The
angles of elevation of the top of pillars are 60o and 30o at a point on the roadway between the
pillars. Find the position of the point between the pillars and the height of each pillar.
Answer: 64.95m
10. At the foot of mountain, the elevation of its peak is 45 o. After ascending 1 km towards the
mountain up an inclination of 30o, the elevation changes to 60o. Find the height of mountain.
Answer: 1.366 km
11. From the top of the building 15m high, the angle of elevation of the top of a tower is found
to be 30o. From the bottom of the same building, the angle of elevation of the top of tower is
found to be 30o. Find the height of the tower and the distance between the tower and the
building.
Answer: 22.5m, 12.975m
12. A fire in a building B is reported on the telephone to two fire stations P and Q, 10 km apart
from each other on a straight road. P observes that the fire is at angle of 60 o to the road and
Q observe that it is an angle of 45o to the road. Which station should send its team and how
much this team has to travel?
Answer: P, 7.32km
13. The shadow of a flagstaff is three times as long as the shadow of the flagstaff when the
sunrays meet the ground at an angle of 60o. Find the angle between the sunrays and the
ground at the time of long shadow.
Answer: 30o
14.From a point in the cricket ground, the angle of elevation of a vertical tower is found to be θ
at a distance of 200m from the tower. On walking 125 m towards the tower the angle of
elevation becomes 2θ. Find the height of tower. (100m)
15. A boy standing on the ground and flying a kite with 75 m of string at an elevation of
45o. Another boy is standing on the roof of 25 m high building and is flying his kite at an
elevation of 30o. Both the boys are on the opposite side of the two kites. Find the length of the
string that the second boy must have, so that the kites meet.(56.05 m)
16. As observed from the top of light house, 100m high above the sea level, the angle of
depression of a ship, sailing directly towards it, changes from 30 o to 45o. Determine the distance
traveled by the ship during the period of observation. Answer: 73.2m
17. An aeroplane at an altitude of 200 m observes the angle of depression of opposite points
on two banks of a river to be 45o and 60o. Find the width of the river. ( 315.4m)
18. From the top of a cliff 150m high, the angles of depression of two boats are 60 o and 30o.
Find the distance between the boats, if the boats are (i) on the side of cliff. (ii) on the
opposite sides of the cliff.
Answer: (i) 173.2m (ii) 346.4m ]
19. A man standing on the deck of a ship, which is 10m above the water level, observe the
angle of elevation of the top of a hill as 60o and the angle of depression of the base of the
hill as 30o.Calculate the distance of the hill from the ship and the height of the hill.
Answer: 17.3m, 40m].
20. The angle of elevation and depression of the top and the bottom of a light house from the
top of the building, 60m high, are 30o and 60o respectively. Find (i) The difference between the
heights of the light house and the building (ii) Distance between the light house and the
building.
Answer: (i) 20m, (ii) 34.64m
21.A pole 5m high is fixed on the top of a tower. The angle of elevation of the top of the pole
observed from Point ‘A’ on the ground is 60o and the angle of depression of the point ‘A’ from
the top of tower is 45o. Find the height of tower.
Answer: 6.83m
22. Man on a cliff observes a boat at an angle of depression of 30o which is approaching the
shore to the point immediately beneath the observer with a uniform speed. Six minutes later, the
angle of depression of the boat is found to be 60o. Find the time taken by the boat to reach
the shore.
Answer: 9 minutes
23. A man on the top of a vertical observation tower observes a car moving at a uniform speed
coming directly towards it. If it takes 12 minutes for the angle of depression to change from
30o to 45o, how soon after this will the car reach the observation tower. Give your answer
correct to nearest seconds.
Answer: 16 min. 24 sec

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Class 10 Application of Trigonometry [Height and Distance] Test paper-02

elevation of the sun.

of 30 m from the root. Find the total height of the tree.

the top of the pole.

correct up to two decimal places.

Answer: (i) 34.64m (ii) 20m

that at that instant.

height of the hill..

find the height of the tree.

Answer: 22.5m, 12.975m

much this team has to travel?

ground at the time of long shadow.

elevation becomes 2θ. Find the height of tower. (100m)

traveled by the ship during the period of observation. Answer: 73.2m

opposite sides of the cliff.

Answer: (i) 173.2m (ii) 346.4m ]

Answer: 17.3m, 40m].

Answer: (i) 20m, (ii) 34.64m

the top of tower is 45o. Find the height of tower.

correct to nearest seconds.

Answer: 16 min. 24 sec

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