SOME APPLICATIONS OF TRIGONOMETRY Test-01

This is SOME APPLICATIONS OF TRIGONOMETRY Test-01 for CBSE class 10 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

The angle of elevation of the top of a tower from a point on the ground and at a distance of 30m from its foot is \(30^\circ \). The height of the tower is

A
\(30\sqrt 3 \) m
B
10 m
C
30 m
D
\(10\sqrt 3 \)m
Correct

From a point on the ground which is 15m away from the foot of a tower, the angle of elevation is found to be \(60^\circ \). The height of the tower is

A
\(20\sqrt 3 \)m
B
\(10\)m
C
\(15\sqrt 3 \)m
Correct
D
\(10\sqrt 3 \)m

From a point P on the level ground, the angle of elevation of the top of a tower is \(30^\circ \). If the tower is 100m high, the distance between P and the foot of the tower is

A
\(150\sqrt 3 \)m
B
\(300\sqrt 3 \)m
C
\(200\sqrt 3 \)m
D
\(100\sqrt 3 \)m
Correct

If the angle of depression of an object from a 75m high tower is \(30^\circ \), then the distance of the object from the tower is

A
\(75\sqrt 3 \)m
Correct
B
\(25\sqrt 3 \)m
C
\(100\sqrt 3 \)m
D
\(50\sqrt 3 \)m

A ladder 14m long rests against a wall. If the foot of the ladder is 7m from the wall, then the angle of elevation is

A
\(45^\circ \)
B
\(75^\circ \)\(45^\circ \)
C
\(60^\circ \)
Correct
D
\(30^\circ \)

If the length of the shadow of a tower is \(\sqrt 3 \) times that of its height, then the angle of elevation of the sun is

A
\(60^\circ \)
B
\(30^\circ \)
Correct
C
\(45^\circ \)
D
\(75^\circ \)

In a \(\Delta ABC\) right angled at B, \(\angle A{\text{ }} = {\text{ }}30^\circ \) and AC = 6cm, then the length of BC is

A
\(3\sqrt 3 \)cm
B
\(2\sqrt 3 \)cm
C
\(4\sqrt 3 \)cm
D
3cm
Correct

If a kite is flying at a height of \(10\sqrt 3 \)m from the level ground attached to a string inclined at \(60^\circ \) to the horizontal then the length of the string is

A
20 m
Correct
B
\(60\sqrt 3 \)m
C
\(80\sqrt 3 \)m
D
\(40\sqrt 3 \)m

The top of a broken tree has its top touching the ground at a distance of 10m from the bottom. If the angle made by the broken part with the ground is \(30^\circ \), then the length of the broken part is

A
\(10\sqrt 3 m\)
B
\(20\sqrt 3 m\)
C
\(20m\)
D
\(\frac{{20}}{{\sqrt 3 }}m\)
Correct

An electric pole is \(10\sqrt 3 \)m high and its shadow is 10m in length, then the angle of elevation of the sun is

A
\(15^\circ \)
B
\(60^\circ \)
Correct
C
\(45^\circ \)
D
\(30^\circ \)

A kite is flying at a height of 60m from the level ground, attached to a string inclined at 30° to the horizontal. The length of the string is

A
120m
Correct
B
\(60\sqrt 3 \)m
C
60m
D
\(40\sqrt 3 \)m

A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. If the angle made by the rope with the ground level is 30°, then the height of the pole is

A
20m
B
\(10\sqrt 3 \)m
C
10m
Correct
D
\(20\sqrt 3 \)m

A river is 60m wide. A tree of unknown height is on one bank. The angle of elevation of the top of the tree from the point exactly opposite to the foot of the tree, on the other bank, is 30°. The height of the tree is

A
\(20\sqrt 3 \)m
Correct
B
\(10\sqrt 3 \)m
C
\(30\sqrt 3 \)m
D
\(60\sqrt 3 \)m

A bridge across a river makes an angle of 45° with the river bank. If the length of the bridge across the river is 200m, then the breadth of the river is

A
200m
B
\(100\sqrt 2 \)m
Correct
C
\(200\sqrt 2 \)m
D
100m

The upper part of a tree broken by the wind falls to the ground without being detached. The top of the broken part touches the ground at an angle of 30° at a point 8m from the foot of the tree. The original height of the tree is

A
8 m
B
24 m
C
\(24\sqrt 3 \)m
D
\(8\sqrt 3 \)m
Correct