CBSE Class 10 Mathematics Introduction to Trigonometry MCQs Set 03

Question. Find the value sin² 30° cos² 45° + 4tan² 30° + 1/2 sin² 90^o 2cos² 90° + 1/24
(a) 1
(b) 2
(c) √2
(d) √3

Answer: B

Question. An electric pole is 10√3 m high and its shadow is 10 m in length, then the angle of elevation of the sun is
(a) 45°
(b) 15°
(c) 30°
(d) 60°

Answer: D

Question. A kite is flying at a height of 90 m above the groun(d) The string attached to the kite is temporarily tied to a point on the groun(d) The inclination of the string with the ground is 60° . The length of the string, assuming that there is no slack in the string is
(a) 90√3 m
(b) 60√3 m
(c) 90 m
(d) 45 m

Answer: B

Question. If the angle of depression of a car from a 100 m high tower is 45°, then the distance of the car from the tower is
(a) 100 m
(b) 200 m
(c) 100√3m
(d) 100√2m

Answer: A

Question. A kite is flying at a height of 200 m above the groun(d) The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 45°. The length of the string, assuming that there is no slack in the string is
(a) 100 m
(b) 200 m
(c) 200√2 m
(d) 100√2 m

Answer: C

Question. Find the value of 5cos α – 4/3 – 5 sin α – 3 + 5 sin α/4 + 5 cos α .
(a) – 1
(b) 5
(c) 1
(d) 0

Answer: D

Question. Two men are on opposite sides of a tower. They observe the angles of elevation of the top of the tower as 30° and 45° respectively. If the height of the tower is 100m, then the distance between them is
(a) 100(√3−1) m
(b) 100(√3+1) m
(c) 100(1−√3) m
(d) none of these

Answer: B

Question. The ___________ is the angle between the horizontal and the line of sight to an object when the object is below the horizontal level.
(a) angle of projection
(b) angle of elevation
(c) None of these
(d) angle of depression

Answer: D

Question. The ratio between the height and the length of the shadow of a pole is √3: 1, then the sun’s altitude is
(a) 45°
(b) 30°
(c) 75°
(d) 60°

Answer: D

Question. The angle of elevation of the top of a tower from a point on the ground and at a distance of 30°m from its foot is . The height of the tower is
(a) 30√3m
(b) 10 m
(c) 10√3m
(d) 30 m

Answer: C

Question. If 8 tan A =15, find the value of sinA – cosA / sinA + cosA
(a) 7/23
(b) 11/23
(c) 13/23
(d) 17/23

Answer: A

Question. If 4sinΘ = 3cosΘ ,find sec²Θ / 4(1 – tan²Θ)
(a) 25/16
(b) 25/28
(c) 1/4
(d) 5/6

Answer: B

Question. Find the value of cos1^o cos2^o cos3^o …..cos89^o cos90^o
(a) 1
(b) 1/2
(c) 1/√2
(d) 0

Answer: D

Question. If tan 26^o tan19^o/ x(1 tan 26^o tan19^o ) = cos60^o, what is the value of x ?
(a) 1
(b) 2
(c) 2
(d) 3

Answer: C

Question. If the shadow of a tower is 30 m long when the sun’s elevation is . The length of the shadow, when the sun’s elevation is
(a) 10 m
(b) 30 m
(c) 10√3 m
(d) 20 m

Answer: A

Question. What is the angle between the hour and minute hands of a clock at 02 :15 hours?
(a) 15^o
(b) 7 (1o/2)
(c) 22(1o/2)
(d) 30^o

Answer: C

Question. Fill in the blanks.

Question. If cosθ =1, then θ = ___________.
Answer: 0

Question. sin58°/cos32° = _____________.
Answer: 1

Question. 3tan²45° = ___________.
Answer: 3

Question. The word ‘Trigonometry’ is derived from the Greek words _____________, _____________ and _____________.
Answer: Tri, gon, metron

One words

Question. What is the relation between sinθ,cosθ and cotθ?
Answer: cotθ= cosθ /sinθ

Question. Does the value of tanq increase or decrease as we increase the value of θ? Give reason.
Answer: Increase because as we increase q, the side opposite to right angle will increase and the ratio of tanq will also increase.

Question. What is the relation between tanq and secθ?
Answer: 1 +tan² θ = sec ² θ

Question. What is the maximum possible value for sine of any angle?
Answer: 1

Question. What is the value of sine of 0°?
Answer: 0

Question. What is 1+tan2θ?
Answer: sec ² θ

Write True or False.

Question.secA =1/cosA = 1 , for an acute θ
Answer: True

Question. The value of tan A is always less than 1. State True or False.
Answer: False

Question. sin60° = 2sin30°
Answer: False

Question. tan² A = sec ² A -1 (v) sin² 56° +cos² 34° =1
Answer: True

Question. cosec 50° = sec 40°
Answer: False

Question. cos A = cos × A
Answer: False