Knowledge Check : Trigonometry
Knowledge Check
Introduction to Trigonometry
Q1: In a right triangle, the side opposite to angle θ is always
A) Adjacent side
B) Hypotenuse
C) Opposite side
D) Base
Q2: The longest side in a right-angled triangle is
A) Opposite side
B) Adjacent side
C) Hypotenuse
D) Any side
Q3: In △ABC right-angled at C, for ∠A the hypotenuse is
A) AB
B) BC
C) AC
D) None
Q4: Sin θ is defined as
A) Adjacent/Hypotenuse
B) Opposite/Hypotenuse
C) Hypotenuse/Opposite
D) Adjacent/Opposite
Q5: Cos θ is defined as
A) Opposite/Hypotenuse
B) Adjacent/Hypotenuse
C) Hypotenuse/Adjacent
D) Opposite/Adjacent
Q6: Tan θ is equal to
A) Opposite/Adjacent
B) Adjacent/Opposite
C) Hypotenuse/Opposite
D) Hypotenuse/Adjacent
Q7: Cosec θ is equal to
A) 1/sin θ
B) 1/cos θ
C) 1/tan θ
D) sin θ/cos θ
Q8: Sec θ is equal to
A) 1/cos θ
B) 1/sin θ
C) 1/tan θ
D) cos θ/sin θ
Q9: Cot θ is equal to
A) 1/tan θ
B) tan θ
C) sin θ/cos θ
D) cos θ/sin θ
Q10: In a right triangle, if opposite side = 3, adjacent = 4, then hypotenuse is
A) 5
B) 7
C) 6
D) 1
Q11: In a right triangle, sin θ = 5/13. The adjacent side is
A) 12
B) 13
C) 5
D) 60
Q12: In a right triangle, tan θ = 1 means θ is
A) 30°
B) 45°
C) 60°
D) 90°
Q13: In a right triangle with sides 8, 15, 17, sin θ (opposite 8) is
A) 8/17
B) 15/17
C) 17/8
D) 8/15
Q14: In a right triangle, if hypotenuse = 1, opposite = 1/2, then θ is
A) 30°
B) 45°
C) 60°
D) 90°
Q15: In a school playground, a student measures a right triangle with opposite side 5 m, adjacent 12 m. Hypotenuse is
A) 13 m
B) 17 m
C) 10 m
D) 7 m
Q16: In a right triangle, cos θ = adjacent/hypotenuse. If adjacent = √3, hypotenuse = 2, then θ is
A) 30°
B) 45°
C) 60°
D) 90°
Q17: In a right triangle, if opposite = adjacent, then tan θ =
A) 0
B) 1
C) ∞
D) √3
Q18: In a right triangle with sides 7, 24, 25, tan θ (opposite 7) is
A) 7/24
B) 24/7
C) 7/25
D) 25/7
Q19: In a right triangle, if hypotenuse = 13, adjacent = 5, then cos θ is
A) 5/13
B) 13/5
C) 12/13
D) 13/12
Q20: In a right triangle, if opposite = √3, adjacent = 1, then θ is
A) 30°
B) 45°
C) 60°
D) 90°
Core Trigonometric Ratios
Q21: If sin θ = 3/5 and θ is acute, find cos θ.
A) 4/5
B) 5/3
C) 3/4
D) 2/5
Q22: What is the value of tan 45°?
A) 0
B) 1
C) √3
D) 1/√3
Q23: If cos θ = 12/13, then sin θ equals:
A) 5/13
B) 13/12
C) 12/5
D) 1/13
Q24: Which ratio is the reciprocal of cosine?
A) Sine
B) Secant
C) Tangent
D) Cosecant
Q25: The value of sin 30° is:
A) 1/√3
B) √3/2
C) 1/2
D) 0
Q26: If tan θ = 5/12, find sec θ.
A) 13/12
B) 12/13
C) 5/13
D) 13/5
Q27: If sin θ = cos θ, then θ equals:
A) 30°
B) 45°
C) 60°
D) 90°
Q28: The value of cos 60° is:
A) 1/2
B) √3/2
C) 0
D) 1
Q29: If tan θ = cot θ, what is θ?
A) 30°
B) 45°
C) 60°
D) 90°
Q30: If cosec θ = 2, then sin θ equals:
A) 2
B) 1/2
C) √3/2
D) 1
Q31: Which of the following is true?
A) sin 0° = 1
B) cos 0° = 0
C) tan 0° = 0
D) cot 90° = 1
Q32: The reciprocal of tan θ is:
A) cos θ
B) sin θ
C) cot θ
D) sec θ
Q33: sin 90° equals:
A) 0
B) 1
C) 1/2
D) √3/2
Q34: cos 90° is equal to:
A) 1
B) 0
C) -1
D) 1/2
Q35: If sin θ = 0, θ equals:
A) 0°
B) 30°
C) 60°
D) 45°
Q36: If cos θ = 1, θ is:
A) 0°
B) 45°
C) 60°
D) 90°
Q37: Which angle has tan value √3?
A) 30°
B) 45°
C) 60°
D) 90°
Q38: If sec θ = 1, θ is:
A) 45°
B) 0°
C) 60°
D) 90°
Q39: Which identity is correct?
A) sin²θ + cos²θ = 0
B) sin²θ − cos²θ = 1
C) sin²θ + cos²θ = 1
D) sec²θ − tan²θ = 0
Q40: If tan θ = 1, θ is equal to:
A) 30°
B) 45°
C) 60°
D) 90°
Trigonometric Identities
Q41: The value of sin² 45° + cos² 45° is
A) 1/2
B) 1
C) √2
D) 0
Q42: 1 + tan² 30° equals
A) sec² 30°
B) cosec² 30°
C) cot² 30°
D) sin² 30°
Q43: Value of sin² 60° + cos² 60° is
A) 1
B) 0
C) 1/2
D) √3/2
Q44: If sin θ = 3/5, then cos θ =
A) 4/5
B) 3/4
C) 5/4
D) –4/5
Q45: 1 + cot² 45° equals
A) cosec² 45°
B) sec² 45°
C) tan² 45°
D) sin² 45°
Q46: Value of sin² 30° – cos² 30° is
A) 0
B) 1
C) –1/2
D) 1/2
Q47: If tan θ = 1/√3, then sec θ =
A) 2/√3
B) √3/2
C) 2
D) 1
Q48: sin² 0° + cos² 90° equals
A) 1
B) 0
C) 2
D) ∞
Q49: Value of (sin 30° + cos 60° )² + (sin 60° + cos 30° )² is
A) 1
B) 2
C) 0
D) 4
Q50: If cos θ = 5/13, then tan θ =
A) 12/5
B) 5/12
C) 13/12
D) 12/13
Q51: In a school exam, sin θ = 8/17, then cos θ + sin θ =
A) 17/17
B) 15/17 + 8/17
C) 25/17
D) 1
Q52: Value of sec² 45° – 1 equals
A) tan² 45°
B) cot² 45°
C) sin² 45°
D) cos² 45°
Q53: cosec² 30° – cot² 30° equals
A) 1
B) 2
C) 3
D) 4
Q54: If sin θ + cos θ = √2, then sin θ cos θ =
A) 1/2
B) 0
C) 1
D) √2/2
Q55: Value of tan 60° × tan 30° is
A) 1
B) √3
C) 1/√3
D) 3
Q56: sin 4θ + cos 4θ + sin² 2θ + cos² 2θ equals
A) 1
B) 2
C) 0
D) 4
Q57: If sin θ = 1/2, then 3 sin θ – 4 sin³ θ equals
A) sin 3θ
B) cos 3θ
C) tan 3θ
D) cot 3θ
Q58: Value of sin 90° – θ × cos θ is
A) 1
B) 0
C) sin θ
D) cos θ
Q59: In a village temple, if sin θ = 5/13, then value of cot θ is
A) 12/5
B) 5/12
C) 13/12
D) 12/13
Q60: The identity sin² θ + cos² θ = 1 is true for
A) Only acute angles
B) Only 0° and 90°
C) All real values of θ
D) Only 45°
Heights and Distances
Q61: A flagstaff stands at the top of a tower. The angle of elevation of the top of the flagstaff is 60° and the bottom of the flagstaff is 45°. If the tower height is 10 m, find the flagstaff height.
A) 10(√3 − 1)
B) 10(√3 + 1)
C) 5(√3 − 1)
D) 5(√3 + 1)
Q62: A ladder leans against a wall making 60° with the ground. If its length is 8 m, what is the height of the wall it reaches?
A) 4√3 m
B) 8√3 m
C) 4 m
D) 8 m
Q63: The angle of elevation of a tower from a point is 30°. If the point is 20 m away, find the height of the tower.
A) 10 m
B) 20/√3 m
C) 10√3 m
D) 20√3 m
Q64: A man observes the top of a building at 45° angle of elevation. If he is 15 m away from the building, what is the height?
A) 7.5 m
B) 15 m
C) 15√2 m
D) 30 m
Q65: From a point on the ground, the angle of elevation of top of tower is 60°. If the height of tower is 20 m, find the horizontal distance.
A) 20√3 m
B) 20/√3 m
C) 10√3 m
D) 10 m
Q66: A pole subtends an angle of 30° at a point on the ground. If the point is 10 m away, find the pole height.
A) 10/√3 m
B) 5√3 m
C) 10√3 m
D) 5 m
Q67: The shadow of a tower is 20 m long when the sun’s elevation is 45°. Find the height of the tower.
A) 10 m
B) 20 m
C) 20√2 m
D) 40 m
Q68: A person sees the top of a tree at 60° and its base at 30°. If the height of his eye is 1.5 m and distance from tree is 10 m, find tree height.
A) 10√3 + 1.5 m
B) 20 + 1.5 m
C) 10(√3 − 1) m
D) 10 + 1.5 m
Q69: The angle of depression of a car from a building is 45°. If the height of the building is 20 m, find the distance of car from building.
A) 5 m
B) 10 m
C) 20 m
D) 20√2 m
Q70: A kite is flying at a height of 50 m. If the string makes an angle of 30° with the ground, find the length of the string.
A) 50 m
B) 100 m
C) 100/√3 m
D) 50√3 m
Q71: A pole casts a shadow 15 m long when the sun’s elevation is 60°. Find the height of the pole.
A) 15√3 m
B) 10√3 m
C) 15/√3 m
D) 30 m
Q72: A balloon is observed from the ground at 30°. If its height is 60 m, find the distance from the point of observation.
A) 60√3 m
B) 60/√3 m
C) 120 m
D) 30 m
Q73: From the top of a building 20 m high, the angle of depression of a car is 30°. Find the distance of the car.
A) 20/√3 m
B) 10√3 m
C) 20√3 m
D) 10 m
Q74: A tree and its shadow are in the ratio 1:√3. Find the elevation of the sun.
A) 30°
B) 45°
C) 60°
D) 90°
Q75: A vertical tower subtends angles 30° and 60° at two points on same side. How is the nearer distance compared to farther?
A) 1:2
B) 2:3
C) 1:3
D) 3:2
Q76: The angle of elevation of top of a building increases from 30° to 60° as observer moves 20 m towards it. Find height of building.
A) 10√3 m
B) 15√3 m
C) 20√3 m
D) 30√3 m
Q77: A watch tower subtends 45° at a point on the ground. If its height is 25 m, find the distance from the point.
A) 12.5 m
B) 25 m
C) 50 m
D) 25√2 m
Q78: A balloon is seen at 45° angle of elevation from point A, and at 30° from point B which is 40 m away. Find balloon height.
A) 20(√3 + 1)
B) 20(√3 − 1)
C) 40 m
D) 30√3 m
Q79: A tree subtends equal angles of elevation at two points in line with its base. Distance between points is 20 m. Find tree height.
A) Cannot be determined
B) Equal to 10tanθ
C) 20tanθ
D) Independent of θ
Q80: A building and its reflection in water make an elevation angle of 60° at a point. Find height if horizontal distance is 20 m.
A) 20√3 m
B) 10√3 m
C) 40√3 m
D) 20 m