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Quiz Chapter 9: Solution of Triangles

10 questions · Form 4 Additional Mathematics Bab 9: Solution of Triangles

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Full Question List & Answer Key

Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.

1. In triangle ABC, angle A = 45°, angle B = 60°, and side c = 10 cm. Calculate angle C.

  1. 75°
  2. 85°
  3. 65°
  4. 95°
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Answer: A

Sum of interior angles of a triangle is 180°. Angle C = 180° - (45° + 60°) = 180° - 105° = 75°.

2. When can Heron's Formula be directly applied to calculate the area of a triangle?

  1. When the lengths of all three sides are known
  2. When two sides and the included angle are known
  3. When two angles and one side are known
  4. Only when the triangle is right-angled
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Answer: A

Heron's Formula calculates the area of a triangle purely using the lengths of all three sides (s = a+b+c2).

3. In triangle KLM, k = 6 cm, l = 8 cm, and m = 10 cm. Find angle M.

  1. 90°
  2. 60°
  3. 45°
  4. 120°
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Answer: A

cos M = k² + l² - m²2kl = 6² + 8² - 10²2 × 6 × 8 = 36 + 64 - 10096 = 096 = 0. cos⁻¹(0) = 90°.

4. In triangle ABC, a = 5 cm, b = 6 cm, and c = 7 cm. Calculate the semi-perimeter s used in Heron's Formula.

  1. 9 cm
  2. 18 cm
  3. 8.5 cm
  4. 10 cm
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Answer: A

The semi-perimeter s = a + b + c2 = 5 + 6 + 72 = 182 = 9 cm.

5. In triangle ABC, a = 12 cm, sin A = 0.8, and sin B = 0.6. Find the length of side b.

  1. 9 cm
  2. 16 cm
  3. 10 cm
  4. 15 cm
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Answer: A

By Sine Rule: a / sin A = b / sin B => 120.8 = b0.6 => 15 = b0.6 => b = 15 × 0.6 = 9 cm.

6. If the area of triangle ABC is 20 cm², side a = 8 cm, and side b = 10 cm, find the acute angle C.

  1. 30°
  2. 45°
  3. 60°
  4. 15°
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Answer: A

Area = (12) ab sin C => 20 = (12)(8)(10) sin C => 20 = 40 sin C => sin C = 0.5 => C = 30°.

7. In triangle ABC, side a = 8 cm, side b = 10 cm, and angle A = 35°. How many distinct triangles can be formed?

  1. 2
  2. 1
  3. 0
  4. 3
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Answer: A

Height h = b sin A = 10 sin(35°) ≈ 5.74 cm. Since h < a < b (5.74 < 8 < 10) and angle A is acute, the ambiguous case occurs, resulting in 2 distinct triangles.

8. In triangle PQR, p = 7 cm, q = 9 cm, and angle R = 60°. Calculate the length of side r.

  1. √67 cm
  2. 8 cm
  3. √130 cm
  4. √79 cm
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Answer: A

Using Cosine Rule: r² = p² + q² - 2pq cos R = 7² + 9² - 2(7)(9) cos(60°) = 49 + 81 - 126(0.5) = 130 - 63 = 67. Therefore, r = √67 cm.

9. In triangle ABC, a = 4 cm, b = 5 cm, and c = 6 cm. Find the value of cos A.

  1. 34
  2. 916
  3. 18
  4. 58
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Answer: A

cos A = b² + c² - a²2bc = 5² + 6² - 4²2 × 5 × 6 = 25 + 36 - 1660 = 4560 = 34.

10. Calculate the area of triangle ABC where a = 6 cm, b = 8 cm, and angle C = 30°.

  1. 12 cm²
  2. 24 cm²
  3. 12√3 cm²
  4. 48 cm²
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Answer: A

Area = (12) ab sin C = (12)(6)(8) sin(30°) = 24 × 0.5 = 12 cm².

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