Class: X
Coacepts COACHING INSTTUTE
Committed to Excellence in Education
Code: X_09-A L1-1
Chapter 09- Applications of Trigonometry (Assignment-1)
By: Er. Gazal Gupta
Category - Assignment
1. From the top of atower 100m high, a man observes two cars on the opposite sides of the tower with
angles of depression 45° and 30 ° resp. Find the distance between the cars. (Take y3 =1.732)
2. Two poles of equal height are standing opposite to each other on either side of the road, which is
100m wide. From a point between them on thefoad, the angles of elevation of the top of the
poles are 60° and 30° resp. Find the height of the poles,
3. From apoint on the ground, the angles of elevation of the botom and top of the transmission tower
fixed at the top of a 1Om high building are 30° and 60° respectively. Find the height of the towe.
4. From the top of a 15m high building, the angleof elevation offhe top of acable tower is 60° and the
angle of depression of its foot is 30°. Determine the heightof the tower.
S. From the top of a vertical tower, the angles of depression oftwocars, in thesame straight line with the
base of the tower, at an instant are found to be 45° and 60°. If the c¡rsare.100m apart.and are on the
same side of the tower, find the height of the tower. (Take y3 1732)
6. The angle of elevation of the top of a vertical tower from a point onthe ground is 60°. From another
point 10m vertically above the first, its angle of elevation is 30 Find the height of the tower.
7. The angles of depression of the top and bottom of a 12m tall building, from the top of amulti-storey
building are 30° and 60° resp. Findthe height of the multi storeyed building.
8. The angle of elevation of thetopof abuilding from the foot ofa tower is 30° and the angle of elevation
of the top of the tower from the foot of the building is 60°. If the tower is 50m high, find the height of
the building.
9. The angles of depression of two ships from the top of a light house and on the same side of it are found
to be 450 and 30° resp. If the ships are 200m apart, find the height of the light house.
10. The angle of elevation of the top of ahill at the foot of a tower is 60° and the angle of
depression from
the top of the tower of the foot of the hill is 30° If the tower is 50m high, find the
height of the hill.
11. From the top of a hill, the angles of depression oftwo
consecutive kilometre stones due east are found
to be 30° and 45°, Find the height of the hill.
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12. The shadow ofa tower standing on a
45° than when it is 60°. Find the level ground is found to be 20m longer when the
sun s aliude 1S
height of the tower.
13. Akite is flying at a height of 4Sm
toa point on the ground. The above the ground. The string attached to the kite is
temporarily tiea
string assuming that there is noinclination of the string with the ground is
slack in the string. 60°. Find the length or ne
14. The angles of depression of the
are 45° and 60° resp. Find the top and bottom of a tower as seen from the top of a 603m high cliff
height of the tower.
15. The angles of elevation and
high building are 30° and 60°depression of the top and bottom of a
resp. Find the light house from the top of a 6Om
(i) difference between the heights of the light house and the
(ii) distance between them building
16. The horizontal distance
betweenfwÓ poles is 15m. The angle of
as seen from the top of the
second pole is 30 Ifthe height of thedepression of the top of the first pole
second pole is 24m, find the height of
the first pole. (Take v3 =1.732)
17. Atower stands near an
airport. The
that its tangent is 5/12. Find the angle of elyaión of the tower froma point on the ground is such
120m.
height of the tower, if the distance of the
observer from the tower is
18. A 1.Sm tall boy stands at a
distance of 3m from a lamp post and çasts a
find the height of the lamp post. shadow of 4.5m on the ground,
19. The angle of elevation of an
aeroplane from a point P on the ground is 60°. After a flight of
the angle of elevation changes to 30°If the 20 seconds,
the speed of the aeroplane. aeroplane is flying at a constant height of 1200V3 m, find
20. At a point on the level ground, the angle of
elevation of a
tangent is 5/12.On walking 192m towards the tower, the vertical tower is found to be such that its
the height of the tower. tangent of the angle of elevation is 3/4. Find
21. An aero plane, when flying at a height of
4000m from the
plane at an instant when the angles of elevations of the ground, paSSe_ vertically above another aero
two planes from the same point on the ground
are 60° and 45° resp. Find the vertical distance
between the aero planes at that instant (Take v3 =1.73)
22. A boy observes that the angle of elevation ofa bird
flying at a
on a 20m high building on the opposite side observes the dugledistance of 100m is 30°. A girl standing
of elevation of the same bird to be 45°.
Find the distance of the bird from the girl.
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23. The angle of elevation of acloud from apoint 120m above the lake is 30° and the angle of depression
of its reflection in the lake is 60°. Find the heightof the cloud.
24. The angles of elevation of the top of atower from two points Aand Bat distance of a andb
respectively from the base and in the same straight line with it are complementary. Prove that the
height of the tower is vab.
a.
23. The angle of elevation of the topof atower from a point on the same level as the foot of the tower is
On advancing, 'p' meters towards the foot of the tower, the angle of elevation becomes B. Show that
ptan a tan B1
height 'h' of the tower is given by h= Ltan ß - tan a
m.
Concept
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