Trigonometry (Class 10 Mathematics)

Trigonometry is the study of relationships between sides and angles in triangles and has numerous applications in navigation, surveying, and engineering. U

Trigonometry (Class 10 Mathematics)

Trigonometry is the study of relationships between sides and angles in triangles and has numerous applications in navigation, surveying, and engineering. U

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TL;DR: Trigonometry is the study of relationships between sides and angles in triangles and has numerous applications in navigation, surveying, and engineeri…

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Trigonometry is the study of relationships between sides and angles in triangles and has numerous applications in navigation, surveying, and engineering. U

Trigonometry MCQs with Answers & Explanations

Q1. In a right-angled triangle, sin A =

  1. Hypotenuse / Opposite
  2. Opposite / Hypotenuse ✓ (correct)
  3. Adjacent / Hypotenuse
  4. Opposite / Adjacent

Explanation: Sin A = Opposite / Hypotenuse, which is one of the basic trigonometric ratios.

Q2. If sin A = 3/5 and angle A is acute, then cos A =

  1. 5/4
  2. 3/4
  3. 4/5 ✓ (correct)
  4. 5/3

Explanation: Using sin^2 A + cos^2 A = 1: (3/5)^2 + cos^2 A = 1, so cos^2 A = 16/25, thus cos A = 4/5.

Q3. The value of sin 0 degrees is:

  1. -1
  2. 1/2
  3. 1
  4. 0 ✓ (correct)

Explanation: sin 0 = 0, which is a standard trigonometric value.

Q4. tan A = cot A when A =

  1. 45 degrees ✓ (correct)
  2. 60 degrees
  3. 30 degrees
  4. 90 degrees

Explanation: tan A = cot A when tan A = 1/tan A, which means tan^2 A = 1, so A = 45 degrees.

Q5. If sin A = cos B and A and B are acute angles, then A + B =

  1. 180 degrees
  2. 90 degrees ✓ (correct)
  3. 45 degrees
  4. 60 degrees

Explanation: If sin A = cos B, then A and B are complementary angles, so A + B = 90 degrees.

Q6. The value of sec 60 degrees is:

  1. sqrt(2)
  2. sqrt(3)/2
  3. 2 ✓ (correct)
  4. 2/sqrt(3)

Explanation: sec 60 = 1/cos 60 = 1/(1/2) = 2.

Q7. If tan A = 1/sqrt(3), then A =

  1. 90 degrees
  2. 60 degrees
  3. 45 degrees
  4. 30 degrees ✓ (correct)

Explanation: tan 30 = 1/sqrt(3), so A = 30 degrees.

Q8. sin^2 A + cos^2 A =

  1. 1 ✓ (correct)
  2. 0
  3. 2
  4. -1

Explanation: sin^2 A + cos^2 A = 1 is the fundamental trigonometric identity.

Q9. If a ladder of length 10 m leans against a wall making 60 degrees with the ground, the height at which it touches the wall is:

  1. 5 m
  2. 5sqrt(3) m ✓ (correct)
  3. 10sqrt(3) m
  4. 10 m

Explanation: Height = 10 x sin 60 = 10 x sqrt(3)/2 = 5sqrt(3) m.

Q10. The angle of elevation from a point on the ground to the top of a 20 m building is 30 degrees. The distance from the point to the base of the building is:

  1. 10sqrt(3) m
  2. 40/sqrt(3) m
  3. 20sqrt(3) m ✓ (correct)
  4. 10 m

Explanation: Distance = 20 / tan 30 = 20 / (1/sqrt(3)) = 20sqrt(3) m.

Frequently Asked Questions

What are the complementary angles in trigonometry?

Two angles are complementary if their sum is 90 degrees, and sin A = cos(90 - A) and cos A = sin(90 - A).

How are trigonometric ratios used in solving real-world problems?

Trigonometric ratios are used in problems involving angles of elevation, angles of depression, and heights and distances.

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