arrow_backBack to Study Resources

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

  1. 75°
  2. 85°
  3. 65°
  4. 95°
Show answer

Answer: A

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

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
Show answer

Answer: A

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

3. 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
Show answer

Answer: A

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

4. 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
Show answer

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.

5. 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
Show answer

Answer: A

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

6. 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
Show answer

Answer: A

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

7. 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
Show answer

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.

8. 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°
Show answer

Answer: A

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

9. 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
Show answer

Answer: A

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

10. 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
Show answer

Answer: A

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

Sponsored