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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

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

Full Question List & Answer Key

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1. 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.

2. For a triangle with side lengths a = 3 cm, b = 4 cm, and c = 5 cm, what is the area?

  1. 6 cm²
  2. 12 cm²
  3. 7.5 cm²
  4. 10 cm²
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Answer: A

This is a right-angled triangle since 3² + 4² = 5². Area = (12) × 3 × 4 = 6 cm².

3. 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°.

4. 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.

5. In triangle ABC, side a = 10 cm, side b = 10 cm, and angle C = 60°. What type of triangle is ABC?

  1. Equilateral triangle
  2. Right-angled triangle
  3. Scalene triangle
  4. Obtuse-angled triangle
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Answer: A

Since a = b, base angles A and B are equal. Sum = 180° - 60° = 120°. A = B = 60°. Since all angles are 60°, it is an equilateral triangle.

6. 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.

7. 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.

8. 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).

9. 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.

10. 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.

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