Chapter Exam

Chapter 6: Trigonometry — Online MCQ Test

Q: In a right-angled triangle, sin θ is equal to ______.

Answer: A. opposite side / hypotenuse — The sine ratio is defined as the length of the side opposite to θ divided by the hypotenuse.

Q: Which of the following is a fundamental trigonometric identity?

Answer: C. sin² A + cos² A = 1 — The basic identity connecting sine and cosine is sin² A + cos² A = 1.

Q: If sin A = 3/5 and A is an acute angle, then cos A is

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.

Q: 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

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.

Q: 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

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.

MATHS · CLASS 10th · Tamil Nadu State Board

Practice Chapter 6: Trigonometry with a free chapter-wise online MCQ test for Tamil Nadu State Board CLASS 10th MATHS. 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.

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Chapter 6: Trigonometry — Important Questions & Answers (FAQ)

Frequently asked questions from Tamil Nadu State Board CLASS 10th MATHS — Chapter 6: Trigonometry, with answers and explanations. These are sample questions; the exam has its own separate question set.

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.

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.

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.

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.

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