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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

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

Full Question List & Answer Key

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

1. 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).

2. 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.

3. 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.

4. 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).

5. 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.

6. 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.

7. 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°.

8. 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.

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 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°.

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