RD Sharma Test: Some Applications of Trigonometry - Class 10 MCQ

# RD Sharma Test: Some Applications of Trigonometry - Class 10 MCQ

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## 25 Questions MCQ Test Mathematics (Maths) Class 10 - RD Sharma Test: Some Applications of Trigonometry

RD Sharma Test: Some Applications of Trigonometry for Class 10 2024 is part of Mathematics (Maths) Class 10 preparation. The RD Sharma Test: Some Applications of Trigonometry questions and answers have been prepared according to the Class 10 exam syllabus.The RD Sharma Test: Some Applications of Trigonometry MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for RD Sharma Test: Some Applications of Trigonometry below.
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RD Sharma Test: Some Applications of Trigonometry - Question 1

### 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°. The height of the tower is

Detailed Solution for RD Sharma Test: Some Applications of Trigonometry - Question 1

Hence the height of the tower is 10√3 meters.

RD Sharma Test: Some Applications of Trigonometry - Question 2

### 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°. The height of the tower is

Detailed Solution for RD Sharma Test: Some Applications of Trigonometry - Question 2

Let the height of the tower be h meters.
In triangle AOB tan 60° = AB/OA

Therfore the height of the tower is 15√3 meters

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RD Sharma Test: Some Applications of Trigonometry - Question 3

### From a point P on the level ground, the angle of elevation of the top of a tower is 30°. If the tower is 100m high, the distance between P and the foot of the tower is

Detailed Solution for RD Sharma Test: Some Applications of Trigonometry - Question 3

Let QR be the height of the tower, then QR = 100 mQ And angle of elevation of the top of the tower be ∠PPR = 30°

Therefore, the distance between P and the foot of the tower is 100√3 metres.

RD Sharma Test: Some Applications of Trigonometry - Question 4

If the angle of depression of an object from a 75m high tower is 30°, then the distance of the object from the tower is

Detailed Solution for RD Sharma Test: Some Applications of Trigonometry - Question 4

In triangle ABC,

Therefore, the distance between P and the foot of the tower is 75√3 metres.

RD Sharma Test: Some Applications of Trigonometry - Question 5

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

Detailed Solution for RD Sharma Test: Some Applications of Trigonometry - Question 5

Let AC be the ladder of lenth 14 m and BC = 7 m

Let angle of elevation ∠ACB = θ ∴ cos θ = BC/AC

RD Sharma Test: Some Applications of Trigonometry - Question 6

If the length of the shadow of a tower is √3 times that of its height, then the angle of elevation of the sun is

Detailed Solution for RD Sharma Test: Some Applications of Trigonometry - Question 6

Let AB be the tree and AP be the shadow.
Let AB = x meters. Then AP = x√3 meters
Also ∠APB = θ
In right angled triangle ABP

Therfore the angle of elevation of the Sun is 30°.

RD Sharma Test: Some Applications of Trigonometry - Question 7

In a ΔABC right angled at B, ∠A = 30° and AC = 6cm, then the length of BC is

Detailed Solution for RD Sharma Test: Some Applications of Trigonometry - Question 7

In triangle ABC ∠A = 30°, and AC = 6 cm
Then lenth of BC,

Therfore the lenth of BC is 3 cm.

RD Sharma Test: Some Applications of Trigonometry - Question 8

If a kite is flying at a height of 10√3m from the level ground attached to a string inclined at 60° to the horizontal then the length of the string is

Detailed Solution for RD Sharma Test: Some Applications of Trigonometry - Question 8

Let AB be the length of the string and AC = 100 m
And ∠ABC = 60°
In triangle ABC,

Therefore, the length of the string is 20 m.

RD Sharma Test: Some Applications of Trigonometry - Question 9

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°, then the length of the broken part is

Detailed Solution for RD Sharma Test: Some Applications of Trigonometry - Question 9

Let AB be the broken part of the tree.

Therefore, the length of the broken part of the tree is 20/√3 meters.

RD Sharma Test: Some Applications of Trigonometry - Question 10

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

Detailed Solution for RD Sharma Test: Some Applications of Trigonometry - Question 10

Let AB be the electric pole of height 10√3 m and its shadow be BC of length 10 m And the angle of elevation of the

RD Sharma Test: Some Applications of Trigonometry - Question 11

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

Detailed Solution for RD Sharma Test: Some Applications of Trigonometry - Question 11

Let kite is flying at a height AB = 60 m and angle of elevation = 30°
To find: Length of the string AC

Therefore, the length of string is 120 m.  B C

RD Sharma Test: Some Applications of Trigonometry - Question 12

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

Detailed Solution for RD Sharma Test: Some Applications of Trigonometry - Question 12

In right triangle ABC,

Hence, the the height of the pole is 10 m.

RD Sharma Test: Some Applications of Trigonometry - Question 13

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

Detailed Solution for RD Sharma Test: Some Applications of Trigonometry - Question 13

Let the river BC be the width of 60 m

and angle of elevation = 30°
To find: Height of the tree AC

Therefore, the height of the tree is 20 √3m.

RD Sharma Test: Some Applications of Trigonometry - Question 14

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

Detailed Solution for RD Sharma Test: Some Applications of Trigonometry - Question 14

Let the breath of the river be h meters.

= 100√2 meters Therefore, the breadth of river is

RD Sharma Test: Some Applications of Trigonometry - Question 15

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

Detailed Solution for RD Sharma Test: Some Applications of Trigonometry - Question 15

RD Sharma Test: Some Applications of Trigonometry - Question 16

The angle of elevation of the top of a tower from two points P and Q at distances of ‘a’ and ‘b’ respectively from the base and in the same straight line with it are complementary. The height of the tower is

Detailed Solution for RD Sharma Test: Some Applications of Trigonometry - Question 16

Let TW be the tower of height hh meters and P and Q are two points such that PW = a and QW = b.

RD Sharma Test: Some Applications of Trigonometry - Question 17

The tops of two poles of height 16m and 10m are connected by a wire. If the wire makes an angle of 60° with the horizontal, then the length of the wire is

Detailed Solution for RD Sharma Test: Some Applications of Trigonometry - Question 17

Therefore, the length of the wire is 12 m.

RD Sharma Test: Some Applications of Trigonometry - Question 18

If the shadow of a tower is 30m long, when the sun’s elevation is 30°. The length of the shadow, when the sun’s elevation is 60°is

Detailed Solution for RD Sharma Test: Some Applications of Trigonometry - Question 18

Therefore, the length of the shadow is 10m long.

RD Sharma Test: Some Applications of Trigonometry - Question 19

If the angle of depression of a car from a 100m high tower is 45°, then the distance of the car from the tower is

Detailed Solution for RD Sharma Test: Some Applications of Trigonometry - Question 19

Let the distance of the car from the tower be x meters.45°

Therefore, the distance of the car from the tower is 100 m.

RD Sharma Test: Some Applications of Trigonometry - Question 20

If the length of the shadow of a tower is equal to its height, then the angle of elevation of the sun is

Detailed Solution for RD Sharma Test: Some Applications of Trigonometry - Question 20

Let AB be the tower and AC be its shadow

And AB = AC= x m
Let the angle of elevation of the sun be θ.
Then ∠ACB = θ
In right angled triangle ABC

Therefore, the angle of elevation of the Sun is 45°.

RD Sharma Test: Some Applications of Trigonometry - Question 21

If the height of the tower is √3 times of the length of its shadow, then the angle of elevation of the sun is

Detailed Solution for RD Sharma Test: Some Applications of Trigonometry - Question 21

Let the length of the shadow be x meters.
Then the height of the tower be √3x meter

RD Sharma Test: Some Applications of Trigonometry - Question 22

A ladder 12m long rests against a wall. If it reaches the wall at a height of 6√3m, then the angle of elevation is

RD Sharma Test: Some Applications of Trigonometry - Question 23

A pole 10m high cast a shadow 10m long on the ground, then the sun’s elevation is

Detailed Solution for RD Sharma Test: Some Applications of Trigonometry - Question 23

Let the length of the shadow BC be 10 meters.
Then the height of the tower AB be 10 meter

RD Sharma Test: Some Applications of Trigonometry - Question 24

If altitude of the sun is 60°, the height of a tower which casts a shadow of length 30m is

Detailed Solution for RD Sharma Test: Some Applications of Trigonometry - Question 24

Given: Angle of elevation θ = 60°
Let the height of the tower AB be hmeters.
And the length of the shadow BC is 30 meters.

Therefore the hieght of the tower is 30√3 meters.

RD Sharma Test: Some Applications of Trigonometry - Question 25

The measure of angle of elevation of the top of a tower 75√3m high from a point at a distance of 75m from the foot of the tower in a horizontal plane is

Detailed Solution for RD Sharma Test: Some Applications of Trigonometry - Question 25

Given: distance from a point to the foot of the tower = 75 m and the height of the tower = 75 m

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## Mathematics (Maths) Class 10

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