Practice the AP 10th Class Maths Bits with Answers Chapter 12 Applications of Trigonometry on a regular basis so that you can attempt exams with utmost confidence.

## AP State Syllabus 10th Class Maths Bits 12th Lesson Applications of Trigonometry with Answers

Question 1.

If the angle of elevation of sun is 45°, then the length of the shadow of a 12 m

high tree is …………………

A) 12 √3 m

B) 16 m

C) 12 m

D) \(\frac{12}{\sqrt{3}}\) m

Answer:

C) 12 m

Question 2.

Observe the figure. Length of the ladder = ……………………

A) 5 cm

B) 10 √3 cm.

C) 20 m.

D) 2.5 m

Answer:

B) 10 √3 cm.

Question 3.

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) 12 m

B) 12 √3 m

C) 7. 5 m

D) 6 m

Answer:

A) 12 m

Question 4.

If the shadow of the tree is \(\frac{1}{\sqrt{3}}\) times the height of the tree, then the angle of elevation of the sun is …………………..

A) 45°

B) 30°

C) 70°

D) 60°

Answer:

D) 60°

Question 5.

The angle of elevation of a jet plane from a point A on the ground is 60°. After a flight of 15 seconds, the angle of elevation changes to 30°. If the jet plane is flying at a constant height of 1500 √3 meter, then the speed of the plane is ……………….. m/sec.

A) 200

B) 300

C) 400

D) 100

Answer:

A) 200

Question 6.

The angle of elevation of top of a tower at a distance of 500 m from the foot is 30°. Then the height of the tower is ………………..

A) \(\frac{500}{\sqrt{3}}\)

B) 500 √3

C) \(\frac{3}{500}\)

D) \(\frac{\sqrt{3}}{500}\)

Answer:

A) \(\frac{500}{\sqrt{3}}\)

Question 7.

If altitude of the sun is 60°. Then the height of the tower which is casting a shadow of 30 m. is ………………… m.

A) 61.69

B) 51.69

C) 51.96

D) 41.69

Answer:

C) 51.96

Question 8.

If a 6m height pole casts a shadow 2√3 m long on the ground, then the sun’s angle of elevation is

A) 60°

B) 45°

C) 30°

D) 90°

Answer:

A) 60°

Question 9.

From a point 30m from the foot of a tower, the angle of elevation of the top is 30°. Then the height of the tower is

A) 10 m

B) 10√3 m

C) 15 m

D) 19 m

Answer:

B) 10√3 m

Question 10.

From a ship masthead 150 ft high, the angle of depression of a boat is observed to 45°. Its distance from the ship is

A) 150 ft

B) 75 ft

C) 150√3 ft

D) \(\frac{150}{\sqrt{3}}\) ft

Answer:

A) 150 ft

Question 11.

A ladder of 19m is leaning to a wall making an angle of 60° with the ground. The distance from the foot of the wall to the foot of the ladder is

A) 18m

B) 19m

C) 9m

D) 9.5m

Answer:

D) 9.5m

Question 12.

A boy observes the top of an electronic pole at an angle of elevation of 60°, when the observation point is 8m away from the foot of the pole. Then the height of the pole is

A) 6√3 m

B) 8√3m

C) 10√3m

D) 16√3 m

Answer:

B) 8√3m

Question 13.

Raj ender observes a person standing on the ground from a helicopter at an angle of depression 45°. If the helicopter flies at a height of 50 m from ground, then the distance of the person from Raj ender is

A) 25 √2 m

B) 50 √2 m

C) 75 √2 m

D) None

Answer:

B) 50 √2 m

Question 14.

The angle of elevation of the top of the cliff from a point 300m from its foot is 60°. Then the height of the cliff is

A) 200 √3 m

B) \(\frac{200}{\sqrt{3}}\) m

C) 300√3 m

D) \(\frac{300}{\sqrt{3}}\) m

Answer:

C) 300√3 m

Question 15.

The angle of elevation of the top of a tower from the top and foot of a pole of height 10m are 30° and 60°. Then the height of the tower is

A) 5 m

B) 10 m

C) 15 m

D) 20 m

Answer:

C) 15 m

Question 16.

A 1.5m tall boy casts 2m shadow. At the same instance, a lamppost casts a shadow of 10 m. Then the height of the lamppost is

A) 6.5 m

B) 7.5 m

C) 8.5 m

D) None

Answer:

B) 7.5 m

Question 17.

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 18.

A ladder ‘x’ meters long is laid against a wall making an angle ‘θ ‘ with the ground. If we want to directly find the distance between the foot of the ladder and the 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 19.

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:

C) A, B are at the same distance from the pole.

Question 20.

The angle of elevation of the top of a tower from a point at a distance 40 m from the foot of the tower is 45°. Then the height of the tower is

A) 20 m

B) 40 m

C) 40 √2 m

D) 40 √3 m

Answer:

B) 40 m

Question 21.

The length of the shadow of a tower is equal to its heights, then the angle of elevation of the sun is

A) 90°

B) 70°

C) 60°

D) 45°

Answer:

D) 45°

Question 22.

What is the angle of elevation of the top of a temple of height 10 m. At a point whose distance from the base of the tower is 10 √3 m

A) 30°

B) 60°

C) 45°

D) 90°

Answer:

A) 30°

Question 23.

From the top of a 10 m height tree, the angle of depression of a point on the ground is 30°. Then the distance of the point from the foot of the tree is

A) 10m

B) 10 √3 m

C) \(\frac{10}{\sqrt{3}}\) m

D) 5 √3 m

Answer:

B) 10 √3 m

Question 24.

The angle of elevation of the sun is 45° then the length of the shadow of a 12 m high tree is ………………

A) 12√3

B) 16

C) 12

D) 16 √3

Answer:

C) 12

Question 25.

The length of the shadow is of 5 m height tree whose angle of elevation of the sun is 30° is

A) 5 m

B) √3 m

C) 5 √3 m

D) 10 m

Answer:

C) 5 √3 m

Question 26.

A man observed the top point of a flag staff with an angle of elevation of 45° standing at a distance away from the bottom of the staff . Find the distance between the man and the staff, if the height of the staff is 50 m.

A) 50 m

B) 60 m

C) 30 m

D) 22.5 m

Answer:

A) 50 m

Question 27.

A man observed the top point of a chimney with angle of elevation 60° standing at a distance 90 m. away from the bottom of the chimney. Then the height of the chimney is …………………..

A) \(\frac{90}{\sqrt{3}}\) m

B) \(\frac{45}{\sqrt{3}}\) m

C) 90 √3 m

D) 45 √3 m

Answer:

C) 90 √3 m

Question 28.

A man observed the top of a hill with an angle of elevation of 50° standing at a distance away from the bottom of the hill. If another man stands on the hill, at what angle of depression did he see the first man ?

A) 60°

B) 50°

C) 70°

D) 80°

Answer:

B) 50°

Question 29.

When the sun rays are falling on the earth at an inclination of 45 0 the shadow of a man is 1.5 metres. Man’s height is …………………

A) 1.2 m

B) 1 m

C) 1.5 m

D) 1.732 m

Answer:

C) 1.5 m

Question 30.

Two towers of heights X and Y. A person standing in between X and Y, he observed the top of the tower at an angles of elevation 30° and 60°. Then the value of X : Y is ……………….

A) 3 : 1

B) 1 : √3

C) √3 : 1

D) 1 : 3

Answer:

D) 1 : 3

Question 31.

The length of the shadow of wall of height 8 m is 5 m. At the same time the tower of height is 50 m its length of the shadow is

A) 200 m

B) 80 m

C) 40 m

D) 20 m

Answer:

B) 80 m

Question 32.

If the angle of elevation of the sun is 60° then the ratio of height of a tree with its shadow is

A) 1 : 1

B) 1 : √3

C) √3 : 1

D) 1 : 3

Answer:

C) √3 : 1

Question 33.

The angle of elevation of a top of the tower from a point 120 m. from its foot is 45°. How much the tower is to be raised when the elevation is to be 60° at the same point ?

A) 120 √3 m

B) 120 m

C) 120(√3 + 1) m

D) 120(√3 – 1) m

Answer:

D) 120(√3 – 1) m

Question 34.

A ladder 19 m leaning to wall at 60° with the ground, the distance from foot to the wall is

A) 18 m

B) 19m

C) 9 m

D) 9.5 m

Answer:

D) 9.5 m

Question 35.

From a ship mast head 150 m high the angle of depression of a boat is observed to be 60° its distance from the ship is ………………..

A) 75.5 m

B) 86.55 m

C) 92.55 m

D) 120.5 m

Answer:

B) 86.55 m

Question 36.

a) Srinu said “Angle of elevation is equal to the angle of depression.”

b) Srikanth said “Angle of depression is equal to the angle of elevation.”

A) Only A is True

B) Only B is True

C) Both A and B are True

D) Both A and B are False

Answer:

C) Both A and B are True

Question 37.

Sin (2 × 30°) = 2 Sin 30° statement is

A) True

B) False

C) Can’t say

D) Not defined

Answer:

B) False

Question 38.

Sin a = \(\frac{x}{y}\) ; cos a = \(\frac{\mathrm{a}}{\mathrm{b}}\) then \(\frac{\text { bx }}{\text { ay }}\) represent

A) Tan α

B) cot α

C) sec α

D) cosec α

Answer:

A) Tan α

Question 39.

The length of shadow of a tree of 8 m long. When the son’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 40.

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 30°. Then the height of the tower is

A) 10 √3 m

B) \(\frac{10}{\sqrt{3}}\) m

C) \(\frac{\sqrt{3}}{10}\)

D) \(\frac{10}{2 \sqrt{3}}\) m

Answer:

A) 10 √3 m

Question 41.

In the adjacent figure ‘θ’ is called as angle of

A) elevation

B) distance

C) depression

D) length

Answer:

C) depression

Question 42.

The height of the tower, in the given figure.

A) 45 m

B) 60 m

C) 50 m

D) 90 m

Answer:

B) 60 m

Question 43.

From the adjacent figure

a) Ravi said ‘y = √3’

b) Ramu said ‘y = V3 ‘

c) Kiran said ‘ y = \(\frac {1}{2}\) ‘

Do you agree with whom ? (Or)

With whom do you agree ? ………………..

A) Ravi

B) Kiran

C) Ramu

D) All of them

Answer:

B) Kiran

Question 44.

“A person is flying a kite at an angle of elevation ‘ α ‘ and the length of the thread from his hand to kite is ‘l’ diagram shows this information is

Answer: