Self Assessment

(a) 30o (b) 45° (c) 60°

(Case Based Objective Questions (4 marks) (d) 90°
4. Erom a top of pillar, which is 35 m high
1 Read the passage given below and answer the water, the angle of depression of a boat isabove
45°
the
Find
following questions. the horizontal distance of the boat from the pillar.
Fire Incident
(a) 35 m (b) 17.5 m (c) 70 m (d) 35 m
There is fire incident in the house. The house door
is locked so, the fireman is trying toenter the house 5. The angle of depression from the top of a tower, 15 m
from the window. He place the ladder against the high at a point on the ground, is 30°. The distance of the
wall such that its top reaches the window as shown
in the figure. point from the top of the tower is
(a) 30 m (b) 15 m
(c) 30 3m (d) 15 V3 m
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 45°. The height of the tower
(in metres) is
(a) 15 (b) 30 (c) 3043 (d) 10/3
OR
Aladder makes an angle of 60° with the ground,
Based onabove information, attempt any 4 out of 5 when placed along a wall. If the foot of the ladder is 8
sub parts. m away from the wall, then the length of the ladder is
(i) If window is 6 m above the ground and angle (a) 4 m (b) 8 m (c) 8/3 m (d) 16 m
made by the foot of ladder to the ground is 30°
then length of the ladder is
7 From the given figure, the angle of depression of
(a) 8 m (b) 10 m (c) 12 m (d) 14 m point Cfrom the point P is
(ii) If fireman place the ladder 5 m away from the
wall and angle of elevation is observed to be 30°
then length of the ladder is 30
10 15
(a) 5 m (b) m (c) m (d) 20 m
(ii) If fireman place the ladder 2.5 m away from
the wall and angle of elevation is observed 60 45°
to be 60°, then find the height of the window. A B C
(Take V3 =1.73) (a) 45° (b) 90° (c) 75°
(a) 4.325 m (b) 5.5 m (d) 30°
(c) 6.3 m (d) 2.5 m (VSA Type Questions (1 mark)
(iv) If the height of the window is 8 m above the
The height of apillar is 8 m. What is
ground and angle of elevation is observed to be
45°, then horizontal distance between the foot shadow, when sun's altitude is 30°? the length of its
of ladder and wall is Find the length of a ladder which is
(a) 2 m (b) 4 m (c) 6 m (d) 8m avertical wall by
making an angle ofleaning
30°
against
with
(v) Ifthe fireman gets a 9 m long ladder and window ground and whose foot is 6 maway from the wall.the
is at 6 m height, then how far should the ladder 10. Akite is flying at a
be placed?
height of 100 mfrom the ground.
It is attached to a string
(a) 5 m (b) 3/5m (c) 3 m (d) 4 m inclined at an angle of 45 to
the horizontal. Find the length of the string.
11, If the length of the
Multiple Choice Questions (1 mark)
shadow of a vertical flag staff
is 1//3 of its height, then
elevation. find the sun's angle of
The tower and its shadow are equal in length, then
find the angle of elevationof the sun. o OR
(a) 30° (b) 60o (c) 90° (d) 45° The angle of depression of a car
A lamp post 5 V3 m high casts ashadow 5 m long on ground from the top.of a standing on the
the ground. The sun's elevation at this moment is the distance of the car from75.m tower, is 30°, Find
the base of the tower
(in metres).
 mtG CBSE Champion
MathematicssClaass 10
hill, tthe angles of
202 21. · From the top of a depression of
12. If the angle of
then find the
elevation of the sun is 30 feet height.
150
consecutive kilometre stones D and C
found to be 30° and 60° respectively. Find
due west twareo
cast by a tower of the height
length of the shadow (2 marks) of the hill.
(SAI Type Questions Case Based Questions
long casts a shadow 5 m long.
At the same (4 marks)
8
wall m find the
13. A
shadow50 m long, then 22. An electrician has to repair an electric fautt ex
time, atower casts a
height of tower. pole of height of 8 m. He needs to reach ane
OR 2m below the top of the pole toundertake the rena:
height 30 m work.
the top of a tower of
A man sitting on of adog sitting on
observes the angle of depression the
the distance between
the ground as 60° Find (Use v3 = 1.732)
A

foot of the tower and the dog. 2m

height 48 m and 60 m are
14. The tops of two towers of angle
connected by a string. If the string is making an the
length of
of 60° with horizontal, then find the
string.
15. From a bridge, 35 m high, the angle of depression of
D

a boat is 45° Find the horizontal distance of the boat Based on given information, answer the followine
from the bridge. questions.
(i) What should be the length of ladder, so that it
16. An aeroplane at an altitude of 400 m observes the
angles of depression of opposite points on the two makes an angle of 60° with base?
banks of ariver to be 45° and 60°. Find width of the (ii) What will be the measure of ZBCD when BD and
river.
CD are equal?
(ii) If an electrician wants to reach 4 m below the
SA IIType Questions (3 marks) top of the pole using a ladder which is 443m
17. Aman standingon the deck of a ship, which is 10m away from it, then what angle does it make with
above water level, observes the angle of elevation of the base?
OR
the top of a hillas 60° and angle of depression of the
base of the hillas 30° Find the horizontal distance of If an electrician want to reach the top of the pole
the hill from the ship and height of the hill. of height 12 m, with making an angle 60° with
base, then find the required length of ladder.
18. On the same side of a tower, two objects are located.
When observed from the top of the tower, their (LA TypeQuestions (4/5/6 marks)
angles of depression are 45° and 60°. If the height
of the tower is 100 m, find the distance between the 23. A boy is standing on the ground and flying a kite
objects. [Use V3 =1.73] with a string of length 150 m at an angle of elevation
of 30, another boy is standing on the roof of a 25
OR m high building and is flying his kite at an elevation
The angle of elevation of the top Qof a vertical tower of 45°. Both the boys are on opposite sides of both
the kites. Find the length of the string (in metres
PQfrom apoint Xon the ground is 60°. At apoint R, corrected to two decimal places) the second boy
40 mvertically above X, the angle of elevation is 459. must have so that the two kites meet.
Find the height of the tower PQ.
(Use V2 =1.4142)
19. Two ships are anchored on opposite sides of a
lighthouse. Their angles of depression as observed 24. A man on the top of a vertical tower observes aCar
moving at a uniform speed coming directly towards
from the top of the lighthouse are 30° and 609 The
it. If it takes 12 minutes for the angle of depressioil
line joining the ships passes through the foot of the to change from 30° to 45 how soon after this, Wl
lighthouse. If the height of the lighthouse is 100 m, find
the distance between the ships. the car reach the tower? Give your answer to U
nearest seConds.
(Use v3 = 1.732) 25. The angle of elevation of the top of a tower frol
20. Two pillars of equal heights stand on either side of a point Adue south of the tower is a and tro
a road vwhich is 160 m wide. At a point on the road B due east of the tower is b. If AB =d. show that tn
between the pillars, the angles of elevation of the d
height of the tower is
tops of the pillars are 60° and 30. Find the height of Vcot a +cot?p
each pillar and the position of the point on the road.