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Quiz Chapter 9: Solution of Triangles

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

Question 1 of 10Score: 0

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

Full Question List & Answer Key

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

1. 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.

2. 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°.

3. In triangle ABC, a = 14 cm, b = 10 cm, and included angle C = 150°. Find the area of triangle ABC.

  1. 35 cm²
  2. 70 cm²
  3. 35√3 cm²
  4. 140 cm²
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Answer: A

Area = (12) ab sin C = (12)(14)(10) sin(150°) = 70 × 0.5 = 35 cm².

4. In triangle XYZ, x = 12 cm, angle X = 50°, and angle Y = 70°. Find the length of side y.

  1. 14.72 cm
  2. 11.13 cm
  3. 15.66 cm
  4. 13.25 cm
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Answer: A

Using Sine Rule: y / sin(70°) = 12 / sin(50°) => y = 12 × sin(70°) / sin(50°) = 12 × 0.93970.7660 ≈ 14.72 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. In triangle ABC, angle A = 30°, angle B = 45°, and side a = 8 cm. Find side b.

  1. 8√2 cm
  2. 4√2 cm
  3. 16 cm
  4. 8√3 cm
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Answer: A

Using Sine Rule: b / sin(45°) = 8 / sin(30°) => b / (√22) = 8 / (12) = 16 => b = 16 × (√22) = 8√2 cm.

7. Under what condition does side 'a' NOT form any valid triangle when given angle A (acute) and side b in an SSA scenario?

  1. a < b sin A
  2. a > b
  3. a = b sin A
  4. b sin A < a < b
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Answer: A

If a < b sin A, side 'a' is shorter than the perpendicular height h = b sin A, meaning it cannot reach the baseline to close the shape, so 0 triangles are formed.

8. 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.

9. Which set of given conditions requires the use of the Cosine Rule to find the unknown side?

  1. Two sides and the included angle (SAS)
  2. Two angles and one side (AAS)
  3. Two sides and a non-included angle (SSA)
  4. One side and two interior angles (ASA)
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Answer: A

The Cosine Rule is used when we know two sides and the included angle between them (SAS) or all three side lengths (SSS).

10. In an ambiguous triangle ABC where a = 7 cm, b = 9 cm, and angle A = 40°, the acute angle B₁ is 55.7°. What is the obtuse angle B₂?

  1. 124.3°
  2. 134.3°
  3. 144.3°
  4. 115.7°
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Answer: A

In the ambiguous case, B₂ = 180° - B₁ = 180° - 55.7° = 124.3°.

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