Chapter 6: Trigonometry — Online MCQ Test
MATHS · CLASS 10th · Tamil Nadu State Board
Practice Chapter 6: Trigonometry with a free chapter-wise online MCQ test.
This chapter covers: Trigonometric ratios Trigonometric identities Sine Cosine Tangent Heights and distances Angle of elevation Angle of depression Complementary angles Applications of trigonometry.
AI-generated questions from basic to board-exam level, with instant results and explanations.
Chapter 6: Trigonometry — Important Questions & Answers
In a right-angled triangle, sin θ is equal to ______.
- A. opposite side / hypotenuse
- B. adjacent side / hypotenuse
- C. opposite side / adjacent side
- D. hypotenuse / opposite side
Answer: A. opposite side / hypotenuse
The sine ratio is defined as the length of the side opposite to θ divided by the hypotenuse.
The sine ratio is defined as the length of the side opposite to θ divided by the hypotenuse.
Which of the following is a fundamental trigonometric identity?
- A. sin A + cos A = 1
- B. sin² A - cos² A = 1
- C. sin² A + cos² A = 1
- D. tan² A + cot² A = 1
Answer: C. sin² A + cos² A = 1
The basic identity connecting sine and cosine is sin² A + cos² A = 1.
The basic identity connecting sine and cosine is sin² A + cos² A = 1.
If sin A = 3/5 and A is an acute angle, then cos A is
- A. 5/3
- B. 3/4
- C. 4/5
- D. 5/4
Answer: C. 4/5
Using sin² A + cos² A = 1, cos² A = 1 - 9/25 = 16/25. Since A is acute, cos A = 4/5.
Using sin² A + cos² A = 1, cos² A = 1 - 9/25 = 16/25. Since A is acute, cos A = 4/5.
From the top of a tower, the angle of depression of a car is 30°. The car moves 60 m towards the tower and the angle of depression becomes 60°. The height of the tower is
- A. 30 m
- B. 30√3 m
- C. 60√3 m
- D. 90 m
Answer: B. 30√3 m
Let the height be h. If the initial distance is x, then h/x = 1/√3 and h/(x - 60) = √3. Solving gives h = 30√3 m.
Let the height be h. If the initial distance is x, then h/x = 1/√3 and h/(x - 60) = √3. Solving gives h = 30√3 m.
From the top of a lighthouse 100 m high, the angles of depression of two ships on the same side of it are 45° and 30°. The distance between the ships is
- A. 100(√3 - 1) m
- B. 100(√3 + 1) m
- C. 100√3 m
- D. 200 m
Answer: A. 100(√3 - 1) m
The horizontal distances are 100/tan 45° = 100 m and 100/tan 30° = 100√3 m. Their difference is 100(√3 - 1) m.
The horizontal distances are 100/tan 45° = 100 m and 100/tan 30° = 100√3 m. Their difference is 100(√3 - 1) m.