Unit Test: Some Applications of Trigonometry | Mathematics (Maths) Class 10 PDF Download

Time: 1 hour

M.M. 30

Attempt all questions.

• Question numbers 1 to 5 carry 1 mark each.
• Question numbers 6 to 8 carry 2 marks each.
• Question numbers 9 to 11 carry 3 marks each.
• Question number 12 & 13 carry 5 marks each.

Q1: _______________________ is drawn from the eye of an observer to the targeted object. (1 Mark)

(a) A parallel line
(b) Line of sight
(c) Elevation line
(d) Depression line

Q2: A slope is built against a wall which makes an angle 30° with the ground and the height of the wall is 2 meters. Find the length of the slope in meters. (1 Mark)

a) 2
b) 4
c) 1
d) 3

Q3: The shadow of a tower is equal to its height at 10-45 a.m. The sun’s altitude is (1 Mark)

(a) 30°
(b) 45°
(c) 60°
(d) 90°

Q4: In given figure, the value of CE is (1 Mark)

(a) 12 cm
(b) 6 cm
(c) 9 cm
(d) 6√3 cm 

Q5: When the length of shadow of a vertical pole is equal to √3 times of its height, the angle of elevation of the Sun’s altitude is __________________________. (1 Mark)

Q6: The ratio of the height of a tower and length of its shadow on the ground is √3 : 1 what is the angle of elevation of the sun? (2 Marks)

Q7: A ladder, leaning against a wall, makes an angle of 60° with the horizontal. If the foot of the ladder is 2.5 m away from the wall, find the length of the ladder. (2 Marks)

Q8: An observer 1.5 m tall is 28.5 m away from a tower of height 30 m. Find the angle of elevation of the top of tower from his eye. (2 Marks)

Q9: A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/h. (3 Marks)

Q10: The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of elevation of the top of the tower from the foot of the hill is 30°. If height of the tower is 50 m, find the height of the hill. (3 Marks)

Q11: A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of hill as 30°. Find the distance of the hill from the ship and the height of the hill. (3 Marks)

Q12: At the foot of a mountain the elevation of its summit is 45°, after ascending 1000 m towards the mountain up a slope of 30° inclination, the elevation is found to be 60°. Find the height of the mountain. (5 Marks)

Q13: The angles of elevation and depression of the top and the bottom of a tower from the top of a building, 60 m high, are 30° and 60° respectively. Find the difference between the heights of the building and the tower and the distance between them. (5 Marks)