BASIC 2026
I. Multiple Choice Questions — [1 Mark each]
Type: Identifying Angles (Depression)
Question:
In the given figure, which of the following angles represents
the angle of depression?
Figure shows an observer at the top of a tower looking down
at an object. Angles marked are \(x\) at the object,
\(y\) between the tower and line of sight, and \(z\) between
the horizontal line and line of sight.
(A) \(x\)
(B) \(y\)
(C) \(z\)
(D) \(a\)
Sets
430/1/1 (Q.12)
430/1/2 (Q.6)
430/1/3 (Q.17)
Type: Shadow Length Dynamics
Question:
The length of the shadow of a tower when the sun's altitude
changes from \(30^\circ\) to \(60^\circ\) will:
(A) become shorter
(B) become longer
(C) remain same
(D) be doubled
Sets
430/2/1 (Q.12)
430/2/2 (Q.6)
430/2/3 (Q.17)
Type: Calculating Angle of Elevation from Figure
Question:
In the given figure, the angle of elevation of point \(A\)
from point \(C\) is:
Figure shows a right-angled triangle \(ABC\), with
\(AB = 2\) cm and \(BC = 2\sqrt{3}\) cm.
(A) \(30^\circ\)
(B) \(45^\circ\)
(C) \(60^\circ\)
(D) Cannot be determined
Sets
430/3/1 (Q.12)
430/3/2 (Q.6)
430/3/3 (Q.17)
II. Very Short Answer Questions — [2 Marks each]
Type: Pole and Tower Shadow Comparison
Question:
A vertical pole of height \(10\) m casts a shadow of \(15\) m
on the ground and at the same time, a tower casts a shadow of
\(45\) m on the ground. Find the height of the tower.
Sets
430/3/1 (Q.22a)
430/3/2 (Q.25a)
430/3/3 (Q.23a)
III. Case Study Questions — [4 Marks each]
Case Study 1: Fireman and the Injured Bird
An injured bird is on a building \(15\) m high. A fireman uses
an adjustable ladder making an angle of \(60^\circ\) with the
ground to reach the roof.
(i) [1 Mark]
Find the length of the ladder used to reach the roof.
(ii) [1 Mark]
Find the distance of the point on the ground where the ladder
was placed from the foot of the building.
(iii) [2 Marks]
(a)
If the fireman places the ladder against the opposite wall of
the road making an angle of \(30^\circ\) with the ground to
prevent slipping, find the width of the road.
OR
(b)
Find the length of the ladder used in this new position.
Sets
430/1/1 (Q.36)
430/1/2 (Q.38)
Case Study 2: Kite Festival — Reena and Ravi
Reena's kite is flying at \(60\) m height with string tied to
the ground at \(30^\circ\). Ravi is flying a kite at \(60\) m
height from a \(10\) m high building. Both use the same length
of string. \(\theta\) is the angle of elevation of Ravi's kite
from the rooftop.
(i) [1 Mark]
Find the length of string used by Reena.
(ii) [1 Mark]
Find the value of \(\sin\theta\).
(iii) [2 Marks]
(a)
If \(\theta\) changes to \(60^\circ\) without changing string
length, find the height of Ravi's kite above the ground.
Use \(\sqrt{3}=1.7\).
OR
(b)
What would be the height of Ravi's kite if the string had an
inclination of \(30^\circ\)?
Sets
430/2/1 (Q.36)
430/2/2 (Q.38)
430/2/3 (Q.37)
STANDARD 2026
1. Multiple Choice Questions — [1 Mark]
Type: Finding Heights and Distances — Pole and Wire
Question:
A wire is attached from a point \(A\) on the ground to the top
of a pole \(BC\), making an angle of elevation as \(60^\circ\).
If \(AB=5\sqrt{3}\) m, then length of the wire is:
(A) \(10\) m
(B) \(10\sqrt{3}\) m
(C) \(15\) m
(D) \(\frac{5}{2}\sqrt{3}\) m
Sets
30/5/1 (Q.17)
30/5/2 (Q.10)
30/5/3 (Q.8)
Type: Tower Elevation — Set 1
Question:
A car is moving away from the base of a \(30\) m high tower.
The angle of elevation of the top of the tower from the car
at an instant, when the car is \(10\sqrt{3}\) m away from the
base, is:
(A) \(30^\circ\)
(B) \(45^\circ\)
(C) \(90^\circ\)
(D) \(60^\circ\)
Sets
30/1/1 (Q.11)
30/1/2 (Q.12)
Type: Tower Height — Set 2
Question:
From a point on the ground, which is \(60\) m away from the
foot of a vertical tower, the angle of elevation of the top
of the tower is found to be \(45^\circ\). The height (in
metres) of the tower is:
(A) \(10\sqrt{3}\)
(B) \(30\sqrt{3}\)
(C) \(60\)
(D) \(30\)
Sets
30/2/1 (Q.12)
30/2/2 (Q.16)
30/2/3 (Q.7)
Type: Shadow and Sun's Altitude
Question:
If the length of the shadow of a tower is \(\sqrt{3}\) times
its height, then the sun's altitude is:
(A) \(45^\circ\)
(B) \(30^\circ\)
(C) \(60^\circ\)
(D) \(15^\circ\)
Set
30/3/1 (Q.9)
2. Long Answer Type — [5 Marks]
Type: Kite and Building Observations — Double Observation
Question:
A kite is flying at a height of \(60\) m above the ground level.
Ravi, standing at the roof of the house is holding the string
straight and observes the angle of elevation of kite as
\(30^\circ\). From the bottom of the same building, the angle
of elevation of kite is \(45^\circ\). Find the length of the
string and height of roof from the ground.
Use \(\sqrt{3}=1.73\).
Sets
30/4/1 (Q.34)
30/4/2 (Q.32)
30/4/3 (Q.32)
Type: Opposite Sides Observation
Question:
A boy standing on a horizontal plane is flying a kite with a
string of length \(60\) m, at an angle of elevation of
\(30^\circ\). Another boy standing on the roof of a \(20\) m
high building finds the angle of elevation of the same kite
to be \(45^\circ\). If both the boys are on opposite sides of
the kite, find the distance of the first boy from the base of
the building. Also, find the height of the kite from the
ground.
Use \(\sqrt{3}=1.73\).
Sets
30/1/1 (Q.35)
30/3/1 (Q.35)
Type: Tower and Flagstaff — Flagstaff Wires
Question:
A vertical tower stands on a horizontal plane and is surmounted
by a vertical flagstaff. From a point on the ground \(30\) m
away from the tower, wires are attached to the top and bottom
of the flagstaff making angles of elevation \(60^\circ\) and
\(30^\circ\) respectively. Find the height of the tower and
lengths of the wires attached.
Take \(\sqrt{3}=1.73\).
Set
30/3/2 (Q.32)
3. Case Study Questions — [4 Marks]
Case Study 1: The Elevated Water Tank
The building is \(54\) metres away from the water tank.
From a window \(W\) of the building, the angle of elevation
of the top of the tank is \(45^\circ\) and angle of depression
of its foot is \(30^\circ\).
(i) [1 Mark]
Write a relation between \(d\), the height of window, and \(y\).
(ii) [1 Mark]
Determine the value of \(h\).
(iii) [2 Marks]
(a)
Determine the height of the water tank.
OR
(b)
Find the value of \(x\) and height of the window above ground
level.
Sets
30/5/1 (Q.38)
30/5/2 (Q.36)
30/5/3 (Q.36)
Case Study 2: The Radio Station Tower
A radio station tower was built in two sections \(A\) and \(B\).
The tower is supported by wires from a point \(O\), \(6\) m
away from the base. The angle of elevation of the top of
section \(B\) is \(30^\circ\) and the angle of elevation of
the top of section \(A\) is \(60^\circ\).
(i) [1 Mark]
Find the length of the wire from point \(O\) to the top of
section \(B\).
(ii) [1 Mark]
Find the length of the wire from point \(O\) to the top of
section \(A\).
(iii) [2 Marks]
(a)
Find the distance \(AB\).
OR
(b)
Find the area of \(\triangle OPB\).
Set
30/1/1 (Q.37)
Case Study 3: Tejas and the Approaching Car
Tejas is standing at the top of a building and observes a car
at an angle of depression of \(30^\circ\) as it approaches the
base of the building at a uniform speed. \(6\) seconds later,
the angle of depression increases to \(60^\circ\), and at that
moment, the car is \(25\) m away from the building.
(i) [1 Mark]
What is the height of the building?
(ii) [1 Mark]
What is the distance between the two positions of the car?
(iii) [2 Marks]
(a)
What would be the total time taken by the car to reach the
foot of the building from the starting point?
OR
(b)
What is the distance of the observer from the car when it makes
an angle of \(60^\circ\)?
Sets
30/2/1 (Q.37)
30/2/2 (Q.36)
30/2/3 (Q.38)
CBSE Class 10 Mathematics — Chapter 9 PYQ Collection
Basic + Standard Mathematics | 2026