CBSE Class 10 Mathematics Introduction to Trigonometry MCQs Set 04

Question. The _____________ is the line drawn from the eye of an observer to the point in the object viewed by the observer.
(a) Horizontal line
(b) line of sight
(c) None of these
(d) Vertical line

Answer: B

Question. A pole 10 m high cast a shadow 10 m long on the ground, then the sun’s elevation is
(a) 60°
(b) 15°
(c) 45°
(d) 30°

Answer: C

Question. Find sin³ φ + cos³ φ/sin φ + cos φ .
(a) 1 + sin – cos φ
(b) 1- sinc φ cos φ
(c) 1- sin φ tan φ
(d) 1

Answer: A

Question. lf sinθ + cosθ/sinθ – cosθ = √3 + 1/√3 – 1 find the acute angleθ .
(a) 90°
(b) 45°
(c) 30°
(d) 60°

Answer: D

Question. What is the value of θ tor which tanθ = cotθ ?
(a) 60°
(b) 45°
(c) 90°
(d) 0°

Answer: B

Question. The ___________ of an object is the angle formed by the line of sight with the horizontal when the object is above the horizontal level.
(a) angle of projection
(b) angle of depression
(c) angle of elevation
(d) none of these

Answer: A

Question. From a point on the ground which is 15m away from the foot of a tower, the angle of elevation is found to be 60° . The height of the tower is
(a) 15√3 m
(b) 20√m
(c) 10√m
(d) 10 m

Answer: A

Question. From a point P on the level ground, the angle of elevation of the top of a tower is . If the tower is 100m high, the distance between P and the foot of the tower is
(a) 300√3 m
(b) 150√3 m
(c) 200√3 m
(d) 100√3 m

Answer: D

Question. If the height of the tower is √3 times of the length of its shadow, then the angle of elevation of the sun is
(a) 15°
(b) 30°
(c) 50°
(d) 45°

Answer: C

Question. A ramp for disabled people in a hospital must slope at not more than 30°. If the height of the ramp has to be 1 m, then the length of the ramp be
(a) 3 m
(b) 1 m
(c) 2 m
(d) √3 m

Answer: C

Question. A river is 60 m wide. A tree of unknown height is on one bank. The angle of elevation of the top of the tree from the point exactly opposite to the foot of the tree, on the other bank, is 30°. The height of the tree is
(a) 30√3 m
(b) 10√3 m
(c) 20√3 m
(d) 60√3 m

Answer: C

Question. A plane is observed to be approaching the airport. It is at a distance of 12 km from the point of observation and makes an angle of elevation of 30° there at. Its height above the ground is
(a) 10 km
(b) 12 km
(c) 6 km
(d) none of these

Answer: C

Question. If the altitude of the sun is 60° , the height of a tower which casts a shadow of length 90 m is
(a) 60 m
(b) 90√3 m
(c) 90 m
(d) 60√3 m

Answer: B

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

Answer: D

Question. If cos9α = sinα a and 9α < 90^o, what is the value of tan 5 a?
(a) 1/√3
(b) √3
(c) 1
(d) 1/2

Answer: C

Question. If ΔABC is right angled at C, find the value of cos(A + B) .
(a) 0
(b) 1
(c) 1/2
(d) √3/2

Answer: A

Question. Fill in the blanks.

Question. 5 cos 0° + sin 90° = ___________.
Answer: 6

Question. tan 0° = ___________.
Answer: 0

Question. 2sin²45° = ___________.
Answer: 1

One words

Question. Can the value of cos θ be 5/4 for some angle θ?
Answer: NO

Question. What is tan(90°-A) equal to?
Answer: cot A

Question. What do we call the side opposite to the right angle in a right triangle?
Answer: Hypotenuse

Question. What is the value of cosec 2θ -cot 2θ?
Answer: 1

Question. Name the side adjacent to angle A if ΔABC is a triangle right-angled at B.
Answer: AB

Question. If cot θ = 7/8 check whether 1-tan2θ/1+tan2θ = cos2θ -sin2θ or not.
Answer: LHS = RHS = -15/113

Write True or False.

Question. tanθ increases faster than sinθ as θ increases.
Answer: True

Question. sinθ +cosθ =1
Answer: False

Question. cos75° = cos60° +cos15°
Answer: False

Question. cosθ = 7/6 for some angleθ
Answer: False

Question.If we increase the lengths of the sides of a right triangle keeping the angle between them same, then the values of the trigonometric ratios will also increase. State True or False.
Answer: False