AP 10th Class Maths 9th Chapter Some Applications of Trigonometry Bits

Chapter 9 Some Applications of Trigonometry Bits for 10th Class AP Board

Multiple Choice Questions (MCQs)

Question 1.
Statement (a) : If the below figure, if BC = 20m, then height AB is 11.56 m.

Statement (b) :
tan θ = \(\frac{\mathrm{AB}}{\mathrm{BC}}\) = \(\) PerPendicular BC base
where θ is the ∠ACB.
A) Both a and b are true
B) a istrue, b is false
C) a is false, b is true
D) Both a and b are false
Answer:
A) Both a and b are true

Question 2.
Statement (a) : If the length of shadow of a vertical pole is equal to its height, then the angle of elevation of the sun is 45°.
Statement (b) : According to Pythagoras theorem, h² = l² + b², where h = hypotenuse, l = Length and b = base.
A) Both a and b are true
B) a istrue, b is false
C) a is false, b is true
D) Both a and b are false
Answer:
A) Both a and b are true

Question 3.
A ladder ‘x’ meters long is laid against a well making an angle ‘θ’ with the ground. If we want to directly find the distance between the foot of ladder and foot of the wall, which trigonometrical ratio should be considered?
A) sin θ
B) cos θ
C) tan θ
D) cot θ
Answer:
B) cos θ

Question 4.
Two persons A and B observe the top of a pole at an angle of elevation α and β respectively. If α > β, then ………………. .
A) A is nearer to the pole than B.
B) B is nearer to the pole than A.
C) A, B are at the same distance from the pole
D) Can’t compare their distances.
Answer:
A) A is nearer to the pole than B.

Question 5.
Top of a building was observed at an angle of elevation ‘α’ from a point, which is at distance’d’ meters from the foot of the building. Which trigonometrical ratio should be considered for finding height of buildings
A) tan α
B) sin α
C) cos α
D) sec α
Answer:
A) tan α

Question 6.
If the angle of elevation of sun increases from 0° to 90°, then the length of shadow of the tower ……………. .
A) no change
B) increases
C) decreases
D) can’t be decided
Answer:
C) decreases

Question 7.
The angle of depression from the top of a tower 12 m height, at a point on the ground is 30°. The distance of the point from the top is …………….. .
A) 10 m
B) 12√ 3m
C) 7.5 m
D) None
Answer:
D) None

Question 8.
A ladder touches a wall at a height of 5m. The angle made by the ladder with the ground, if its length is 10 m, will be ……………. .
A) 30°
B) 60°
C) 45°
D) 90°
Answer:
A) 30°

Question 9.
A 20 m long ladder is placed on a pole of 10 m height making ‘α’ angle with the ground, then α =
A) 60°
B) 45°
C) 30°
D) 0°
Answer:
C) 30°

Question 10.
A ladder 15m long just reaches the top of vertical wall. If the ladder makes an angle of 60° with the wall. Then the height of the wall is
A) 15√3m
B) \(\frac{15 \sqrt{3}}{2}\)m
C) 7.5 m
D) 15 m
Answer:
B) \(\frac{15 \sqrt{3}}{2}\)m

Question 11.
If the angle of elevation of Sun increases from 0° to 90°, then the length of the shadow of the tower is …………….. .
A) No change
B) Increases
C) Decreases
D) Can’t be decided
Answer:
C) Decreases

Question 12.
If the ratio of the height of a pole and the length of it’s shadow is √3 : 1, then the angle of elevation of Sun is ………………. .
A) 30°
B) 60°
C) 45°
D) 90°
Answer:
B) 60°

Question 13.
The length of the shadow of a tree is 8 m long when the sun’s angle of elevation is 45° is ……………… m.
A) \(\frac{8}{\sqrt{3}}\)
B) 8√3
C) 8
D) 16√3
Answer:
C) 8

Question 14.
If a pole 6 m high casts a shadow 2√3m long on the ground, then the sun’s angle of elevation is
A) 60°
B) 45°
C) 30°
D) 90°
Answer:
A) 60°

Question 15.
If the angle of elevation of a tower from a distance of 100 m from its foot is 60°, then the height of the tower is ……………… m.
A) 100√3
B) \(\frac{100}{\sqrt{3}}\)
C) 50√3
D) \(\frac{50}{\sqrt{3}}\)
Answer:
A) 100√3

Question 16.
The height of a tower is 10 m. The length of its shadow when sun’s altitude is 45° is …………………… m.
A) 10
B) 20
C) 10√3
D) 50
Answer:
A) 10

Question 17.
The length of the shadow of a tower on the plane ground is √3 times the height of the tower. The angle of elevation of sun is
A) 30°
B) 45°
C) 60°
D) 90°
Answer:
A) 30°

Question 18.
In the given figure, the positions of the observer and the object are marked, the angle of depression is

A) 45°
B) 60°
C) 30°
D) 90°
Answer:
B) 60°

Question 19.
In the given figure, the value of angle θ is

A) 30°
B) 60°
C) 45°
D) 90°
Answer:
A) 30°

Question 20.
The ratio of the length of a rod and its shadow is 1 : √3 then the angle of elevation of the sun is
A) 45°
B) 30°
C) 75°
D) 90°
Answer:
B) 30°

Question 21.
If two towers of height X and Y subtend angles of 30° and 60° respectively at the centre of the line joining their feet, then X : Y is equal to
A) 1 : 3
B) 3 : 1
C) 1 : √3
D) √3 : 1
Answer:
A) 1 : 3

Question 22.
A wall of 8 m long casts a shadow 5 m long. At the same time, a tower casts a shadow 50 m long, then the height of tower is
A) 20 m
B) 80 m
C) 40 m
D) 200 m
Answer:
B) 80 m

Question 23.
If the sun’s angle of elevation is 60°, then a pole of height 6 m will cast a shadow of length ……………… m.
A) √3
B) 5√3
C) 6√3
D) 2√3
Answer:
D) 2√3

Question 24.
A pole of 12 m high casts a shadow 4√3 m on the ground, then the sun’s angle of elevation is
A) 60°
B) 120°
C) 45°
D) 30°
Answer:
A) 60°

Question 25.
If the height and length of the shadow of a man are the same, then the angle of elevation of the sun is
A) 60°
B) 45°
C) 90°
D) 120°
Answer:
B) 45°

Question 26.
The given figure shows the observation of point ‘C’ from point A. The angle of depression from A is

A) 30°
B) 45°
C) 90°
D) 75°
Answer:
A) 30°

Question 27.
If the length of the shadow of a tower is \(\frac{1}{\sqrt{3}}\) times the height of the tower, then the angle of elevation of the sun is ……………… .
A) 30°
B) 45°
C) 60°
D) 75°
Answer:
C) 60°

Question 28.
A tower is 50 m high. Its shadow is x m shorter when the sun’s altitude is 45° then when it is 30°, then x = ………………… cm.
A) 105
B) 20
C) 10
D) 100
Answer:
D) 100

Question 29.
The length of the string of a kite flying at 100 m above the ground with the elevation of 60° is ………………. .
A) \(\frac{200}{\sqrt{3}}\)
B) \(\frac{20}{\sqrt{3}}\)
C) \(\frac{291}{\sqrt{3}}\)
D) Done
Answer:
A) \(\frac{200}{\sqrt{3}}\)

Question 30.
A player sitting on the top of a tower of height 40 m observes the angle of depression of a ball lying on the ground is 60°. The distance between the foot of the tower and ball is ……………….. m.
A) 20
B) \(\frac{80}{\sqrt{61}}\)
C) \(\frac{40}{\sqrt{3}}\)
D) \(\frac{40}{\sqrt{6}}\)
Answer:
C) \(\frac{40}{\sqrt{3}}\)

Question 31.
If the ratio of height of a tower and the length of its shadow on the ground is √3 : 1, then the angle of elevation of the sun is …………….. .
A) 80°
B) 60°
C) 70°
D) 100°
Answer:
B) 60°

Question 32.
The angle of depression of the top of a tower at a point 100 m from the house is 45°, then the height of the tower is ………………. m.
A) 18.1
B) 16.3
C) 36.6
D) 26.7
Answer:
C) 36.6

Question 33.
Suppose you are shooting an arrow from the top of a building at a height of 6 m to a target on the ground at an angle of depression of 60° what is the distance between yOu and the object?
A) 9
B) 7√3
C) 12√3
D) None
Answer:
D) None

Question 34.
tan A = \(\frac{n}{n+1}\), tan B = \(\frac{1}{2 n+1}\) A + B = ……………… .
A) 4
B) 3
C) -1
D) 1
Answer:
D) 1

Question 35.
The angle of elevation of tower at a point 40 m apart from it is cot^-1() Obtain the height of the tower.
A) \(\frac{200}{3}\)m
B) \(\frac{100}{3}\)m
C) \(\frac{210}{17}\)m
D) Done
Answer:
A) \(\frac{200}{3}\)m

Question 36.
A ladder 20 m long is placed against a vertical wall of height 10 m, then the distance between the foot of the ladder and the wall is ……………… m.
A) 7√3
B) 20√3
C) 30√3
D) none
Answer:
C) 30√3

Question 37.
sin 18° = ………………… .
A) \(\frac{\sqrt{5}}{4}\)
B) \(\frac{\sqrt{5}-1}{4}\)
C) \(\frac{1+\sqrt{3}}{2}\)
D) \(\frac{\sqrt{3}-1}{4}\)
Answer:
B) \(\frac{\sqrt{5}-1}{4}\)

Question 38.
In the below figure x = ……………… cm.

A) 10
B) 12
C) 13
D) 19
Answer:
A) 10

Question 39.
cot (90 – A) = ……………… .
A) 3 tan A
C) cot A
B) sin A
D) tan A
Answer:
D) tan A

Question 40.
At a point 15 m away from the base of a 15 m high pole, the angle of elevation of the top is ……………… .
A) 30°
B) 45°
C) 60°
D) 90°
Answer:
B) 45°

Question 41.
When the length of the shadow of a person is equal to his height, then the elevation of source of light is
A) 15°
B) 30°
C) 45°
D) 60°
Answer:
C) 45°

Question 42.
The angle of elevation of top of a tree is 30°. On moving 20 m nearer, the angle of elevation is 60°. The height of the tree is
A) 15√3 m
B) 2√3m
C) 10√3 m
D) 5√3 m
Answer:
C) 10√3 m

Question 43.
The ratio of length of a pole and its shadow is 1 : √3. The angle of elevation is
A) 90°
B) 60°
C) 45°
D) 30°
Answer:
D) 30°

Question 44.
The upper part of a tree is broken by wind and makes an angle of 30° with the ground and at a distance of 21 m from the front of the tree. Find the total height of the tree.
A) 30√3 m
B) 21 m
C) 30 m
D) 21√3 m
Answer:
D) 21√3 m

Question 45.
From a bridge 25 m high, the angle of depression of a boat is 45°. Find the horizontal distance of the boat from the bridge.
A) 25√3 m
B) 25 m
C) \(\)\frac{25}{\sqrt{3}}\(\) m
D) 45 m
Answer:
B) 25 m

Question 46.
A tower makes an angle of elevation equal to the angle of depression from the top of a cliff 25 m heigh. Find the height of the tower.
A) 25 m
B) 75 m
C) 5 m
D) 50 m
Answer:
D) 50 m

Question 47.
In a rectangle, if the angle between a diagonal and a side is 30°, and the length of the diagonal is 6 cm, the area of the rectangle is
A) 18 cm²
B) 9 cm²
C) 18√3 cm²
D) 9√3 cm²
Answer:
D) 9√3 cm²

Question 48.
Two posts are 15 m and 25 m high and the line joining their tops make an angle of 45° with the horizontal. The distance between the two posts is
A) 15 m
B) 25 m
C) 18 m
D) 10 m
Answer:
D) 10 m

Question 49.
An electric pole 20 m high stands up right on the ground with the help of steel wire to its top and affixed on the ground. If the steel wire makes 60° with the horizontal ground, find the length of steel wire.
A) 60√3 m
B) 20 m
C) 60 m
D) \(\)\frac{20}{\sqrt{3}}\(\) m
Answer:
D) \(\)\frac{20}{\sqrt{3}}\(\) m

Question 50.
A building casts a shadow of length 50√3 in when the sun is 30° about the horizontal. The height of the building is
A) 30 m
B) 40 m
C) 50 m
D) 60 m
Answer:
C) 50 m

Question 51.
When the angle of elevation of a light changes from 30° to 45°, the shadow of pole becomes 100√3 m less. The height of the pole is
A) 30 m
B) 120 m
C) 75 m
D) 100 m
Answer:
D) 100 m

Question 52.
From the top of a building 50 m from horizontal, the angle of depression made by a car is 30°. How far is the car from the building ?
A) \(\)\frac{50}{\sqrt{3}}\(\) m
B) 50√3 m
C) 150 m
D) 30√3 m
Answer:
B) 50√3 m

Question 53.
From the top of a building with height 30 (√3 + 1) m two cars make angles of depression of 45° and 30° due east. What is the distance between two cars?
A) 30 m
B) 60 m
C) 45 m
D) 75 m
Answer:
B) 60 m

Question 54.
A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 60°. When he retires 40 m from the bank, he finds the angle to be 30°. The breadth of the river is
A) 10 m
B) 15 m
C) 20 m
D) 25 m
Answer:
C) 20 m

Question 55.
A ladder of 10 m length touches a wall at a height of 5 m. The angle made by it with the horizontal is
A) 30°
B) 45°
C) 60°
D) 90°
Answer:
A) 30°

Question 56.
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with the ground. The distance between the top of the tree and the ground is 10 m. Find the height of the tree.
A) 10 m
B) 30√3 m
C) 10√3 m
D) 30 m
Answer:
C) 10√3 m

Question 57.
The angle of elevation of a cloud from a point 200 m above the lake is 30° and the angle of depression of its reflection in the lake is 60°. The height of the cloud above the lake is
A) 100 m
B) 200 m
C) 300 m
D) 400 m
Answer:
D) 400 m

Question 58.
An aeroplane flying horizontally 1 km above the ground is observed at an elevation of 60°. After a flight of 10 seconds, its angle of elevation is observed to be 30° from the same point on the ground. Find the speed of the aeroplane.
A) 415.7 km/h
B) 215.3 km/h
C) 700 km/h
D) none of the above
Answer:
A) 415.7 km/h

Question 59.
If AB = 4 m, and AC = 8 m, then the angle of elevation of A as observed from C is
A) 30°
B) 45°
C) 60°
D) 90°
Answer:
A) 30°

Question 60.
If the shadow of a tree is \(\)\frac{1}{\sqrt{3}}\(\) times the height of the tree, then the angle of elevation of the sun is
A) 30°
B) 45°
C) 60°
D) 90°
Answer:
C) 60°

10th Class Maths Bits