FSc Part 1 Maths chapter 12: Application of trigonometry MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

20 exam-style questions on Application of trigonometry, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

20 questions · 2 topics · 10 per test

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What chapter 12 covers

Ten Application of trigonometry questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. In triangle ABC, a = 6, b = 8 and γ = 30°. The area of the triangle is

  1. A
    24
  2. B
    12
  3. C
    12√3
  4. D
    48
Show answer

Answer: B. Δ = ½ab sin γ = ½ × 6 × 8 × ½ = 12. Using cos 30° instead of sin 30° gives 12√3.

2. In triangle ABC with sides a, b, c opposite angles α, β, γ, the law of cosines gives

  1. A
    a2 = b2 + c2 − 2bc cos α
  2. B
    a2 = b2 + c2 + 2bc cos α
  3. C
    a2 = b2 + c2 − 2ab cos α
  4. D
    a2 = b2 − c2 − 2bc cos α
Show answer

Answer: A. The angle in the formula is the one between the two sides b and c, opposite to a. When α = 90° it reduces to Pythagoras.

3. The area of an equilateral triangle with side 4 cm is

  1. A
    16 cm2
  2. B
    8√3 cm2
  3. C
    4√3 cm2
  4. D
    2√3 cm2
Show answer

Answer: C. Δ = ½ab sin 60° = ½ × 4 × 4 × √3/2 = 4√3 cm2.

4. The area of a triangle with sides 5, 12 and 13, found by Hero's formula, is

  1. A
    30
  2. B
    60
  3. C
    15
  4. D
    65
Show answer

Answer: A. s = 15, Δ = √(15 × 10 × 3 × 2) = √900 = 30. It is right-angled, so ½ × 5 × 12 = 30 agrees.

5. In triangle ABC, a = 3, b = 4, c = 5. Using sin(γ/2) = √((s − a)(s − b)/ab), the value of sin(γ/2) is

  1. A
    1/2
  2. B
    1/√2
  3. C
    √3/2
  4. D
    1/√3
Show answer

Answer: B. s = 6, so sin(γ/2) = √((3)(2)/(12)) = √(1/2) = 1/√2. Then γ/2 = 45° and γ = 90°, as expected for a 3-4-5 triangle.

6. From a point 50 m from the foot of a vertical tower on level ground, the angle of elevation of the top is 30°. The height of the tower is about

  1. A
    25 m
  2. B
    86.6 m
  3. C
    28.9 m
  4. D
    43.3 m
Show answer

Answer: C. tan 30° = h/50, so h = 50/√3 ≈ 28.9 m. Using tan 60° gives 86.6 m; 25 m and 43.3 m use sin and cos wrongly.

7. The law of tangents states that (a − b)/(a + b) is equal to

  1. A
    tan((α − β)/2) / tan((α + β)/2)
  2. B
    tan((α + β)/2) / tan((α − β)/2)
  3. C
    sin((α − β)/2) / sin((α + β)/2)
  4. D
    tan(α − β) / tan(α + β)
Show answer

Answer: A. (a − b)/(a + b) = tan((α − β)/2)/tan((α + β)/2): difference over sum on both sides, using half-angles.

8. The in-radius of a triangle with sides 3, 4 and 5 is

  1. A
    2.5
  2. B
    2
  3. C
    1
  4. D
    6
Show answer

Answer: C. Δ = 6 and s = 6, so r = Δ/s = 1. 2.5 is the circum-radius and 6 is the area.

9. In any triangle ABC, the circum-radius R is equal to

  1. A
    a/sin α
  2. B
    2a sin α
  3. C
    a/(2 sin α)
  4. D
    abc/Δ
Show answer

Answer: C. From the law of sines, a/sin α = 2R, so R = a/(2 sin α). Equivalently R = abc/(4Δ), not abc/Δ.

10. The in-radius of a triangle with sides 13, 14 and 15 (area 84) is

  1. A
    2
  2. B
    4
  3. C
    8
  4. D
    65/8
Show answer

Answer: B. r = Δ/s = 84/21 = 4, where s is the semi-perimeter. Dividing by the full perimeter 42 gives 2.

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Ways to practise this chapter

Application of trigonometry: questions students ask

How many Application of trigonometry MCQs are there?

20, each with the answer and a short explanation, across 2 topics: Solving triangles, Area of a triangle and connected circles. Every chapter test draws ten of them, so you can take it many times.

Is the FSc Part 1 Maths chapter 12 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

Can I read the explanations in Urdu?

Yes. In practice mode and on your results you can switch the explanations to Urdu.

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