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Quiz Chapter 9: Solution of Triangles

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

10 questions · plays in fullscreen

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 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.

2. 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°.

3. Given triangle PQR with p = 5 cm, q = 7 cm, and r = 9 cm. Find cos P.

  1. 2942
  2. 1114
  3. 35
  4. 1921
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Answer: A

cos P = q² + r² - p²2qr = 7² + 9² - 5²2 × 7 × 9 = 49 + 81 - 25126 = 105126 = 2942 (or 56).

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. 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).

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. 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).

8. 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°.

9. 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.

10. 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.

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