CBSE Class 10 Mathematics Trigonometry Assignment Set A

Question. The angle of elevation of the Sun when the shadow of a pole h m high is 3 h m long is
(a) 0°
(b) 30°
(c) 45°
(d) 60°
Answer : B

Question. 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, then the height of pole, if the angle made by the rope with the ground level is 30°, is
(a) 5 m
(b) 10 m
(c) 15 m
(d) 20 m
Answer : B

Question. A kite is flying at a height of 80 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with ground is 60°, then the length of the string is
(a) 62.37 m
(b) 92.37 m
(c) 52.57 m
(d) 72.57 m
Answer : B

Question. From the top of a 60 m high tower, the angle of depression of a point on the ground is 30°. The distance of the point from the foot of tower is
(a) 180 m
(b) 60 3 m
(c) 150 m
(d) 30 3 m
Answer : B

Question. The figure shows the observation of point C from point A. The angle of depression fromA is
(a) 30°
(b) 45°
(c) 60°
(d) 90°
Answer : A

Question. If a pole 6 m high casts a shadow2 3m long on the ground, then the Sun’s elevation is
(a) 60°
(b) 45°
(c) 30°
(d) 90°
Answer : A

Question. If 300 3m high tower makes an angle of elevation at a point on ground which is 300 m away from its foot, then the angle of elevation is
(a) 0°
(b) 30°
(c) 45°
(d) 60°
Answer : D

Question. A ramp for disabled people in a hospital have slope 30°. If the height of the ramp be 1m, then the length of ramp is
(a) 2 m
(b) 0.5 m
(c) 2 3m
(d) 1 m
Answer : A

Question. The angle of depression of the car parked on the road from the top of a 150 m high tower is 30°. The distance of the car from the tower is 
(a) 150 m
(b) 75 m
(c) 150√3m
(d) (150/√3)m
Answer : C

Question. The length of a string between a kite and a point on the ground is 85 m. If the string makes an angle θ with the ground level such that tanθ = 15/8 , then the height of kite is
(a) 75 m
(b) 78.05 m
(c) 226 m
(d) None of these
Answer : A

Question. A tower stands near an airport. The angle of elevation θ of the tower from a point on the ground is such that its tangent is 5/12. The height of the tower, if the distance of the observer from the tower is 120 m is
(a) 40 m
(b) 50 m
(c) 60 m
(d) 70 m
Answer : B

Question. The top of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle of 30° with the horizontal, then the length of the wire is
(a) 12 m
(b) 10 m
(c) 8 m
(d) 6 m
Answer : A

Question. A ladder, leaning against a wall,makes an angle of 60° with the horizontal. If the foot of the ladder is 9.5m away from the wall. The length of the ladder is
(a) 10 m
(b) 16 m
(c) 18 m
(d) 19 m
Answer : D

Question. From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively, then the height of the tower is
(a) 14.64 m
(b) 28.64 m
(c) 38.64 m
(d) 19.64 m
Answer : A

Question. An observer, 1.5 m tall is 20.5 m away from a tower 22 m high, then the angle of elevation of the top of the tower from the eye of the observer is
(a) 30°
(b) 45°
(c) 60°
(d) 90°
Answer : B

Question. The angle of elevation of the top of the tower from a point, which is 40 m away from the base of the tower in the horizontal level, is 45°. Find the height of the tower.
(a) 70 m
(b) 60 m
(c) 40 m
(d) 30 m
Answer : C

Question. The angle of elevation of the top of a building 150 m high, from a point on the ground is 45°. The distance of the point from foot of the building is
(a) 120 m
(b) 130 m
(c) 140 m
(d) 150 m
Answer : D

Question. A bridge on a river makes an angle of 45° with its edge. If the length along the bridge from one edge to the other is 150 m, then the width of the river is
(a) 107.75 m
(b) 105 m
(c) 75 m
(d) 106.05 m
Answer : D

Case Based MCQs

A. There are two balcony in a house. First balcony is at a height of 3 m above the ground and other balcony is 6 m vertically above the lower balcony. Ankit and Radha are sitting inside the two balcony at points G and F, respectively. At any instant, the angles of elevation of a Parachute from these balcony are observed to be 60° and 45° as shown below

Based on the above information, answer the following questions.

Question. Who is more closer to the Parachute.
(a) Ankit
(b) Radha
(c) Both are at equal distance
(d) Can’t be determined
Answer : B

Question. Value of DF is equal to
(a) (h/√3)m
(b) h√3m
(c) (h/2)
(d) h m
Answer : D

Question. Value of h is
(a) 2
(b) 3(√3 + 1)
(c) 4
(d) 3(√3 − 1)
Answer : B

Question. Height of the Parachute from the ground is
(a) 4 m
(b) 3(4− √3)
(c) 8 m
(d) 3(4 + √3)
Answer : D

Question. If the Parachute is moving towards the building, then both angles of elevation will
(a) remain same
(b) increases
(c) decreases
(d) Can’t be determined
Answer : C

B. A cyclist is climbing through a 20 m long rope which is highly stretched and tied from the top of a vertical pole to the ground as shown below Based on the above information, answer the following questions.

Question. The height of the pole, if angle made by rope with the ground level is 60°, is
(a) 15 m
(b) 10√3 m
(c) (10/√3)m
(d) (15/√2)m
Answer : B

Question. If the angle made by the rope with the ground level is 60°, then the distance between artist and pole at ground level is
(a) (10/√2)m
(b) 10√2m
(c) 10 m
(d) 10√3 m
Answer : C

Question. If the angle made by the rope with the ground level is 45°. The height of the pole is
(a) 2.5 m
(b) 10 m
(c) 7.5 m
(d) 10√2 m
Answer : D

Question. If the angle made by the rope with the ground level is 45° and 3 m rope is broken, then the height of the pole is
(a) (17/√2)m
(b) 7 m
(c) 14 m
(d) 7√2 m
Answer : A

Question. Which mathematical concept is used here?
(a) Similar triangles
(b) Pythagoras theorem
(c) Application of trigonometry
(d) None of the above
Answer : C