NBT Mathematics: Geometry and Trigonometry 2 — Questions and Answers
Question 1: A circle has a radius of 7 cm. What is its circumference?
- 14π cm (Correct answer)
- 49π cm
- 7π cm
- 28π cm
Correct answer: 14π cm
Circumference = 2πr = 2π(7) = 14π cm.
Question 2: In triangle ABC, angle A = 35° and angle B = 75°. What is angle C?
- 70° (Correct answer)
- 80°
- 90°
- 60°
Correct answer: 70°
Angles in a triangle sum to 180°, so C = 180° − 35° − 75° = 70°.
Question 3: What is sin(45°)?
- √2/2 (Correct answer)
- √3/2
- 1/2
- 1
Correct answer: √2/2
sin(45°) = √2/2 ≈ 0.707, derived from the 45-45-90 triangle.
Question 4: A rectangle has length 12 m and width 5 m. What is the length of its diagonal?
- 13 m (Correct answer)
- 17 m
- 11 m
- 60 m
Correct answer: 13 m
By the Pythagorean theorem, diagonal = √(12² + 5²) = √(144 + 25) = √169 = 13 m.
Question 5: The bearing of point B from point A is 120°. What is the bearing of A from B?
- 300° (Correct answer)
- 240°
- 060°
- 210°
Correct answer: 300°
The reverse bearing is found by adding or subtracting 180°: 120° + 180° = 300°.
Question 6: Which of the following is the correct cosine rule for triangle ABC?
- a² = b² + c² − 2bc·cos A (Correct answer)
- a² = b² + c² + 2bc·cos A
- a = b·cos C + c·cos B
- a² = b² − c² + 2bc·cos A
Correct answer: a² = b² + c² − 2bc·cos A
The cosine rule states a² = b² + c² − 2bc·cos A.
Question 7: A sector of a circle has radius 6 cm and central angle 60°. What is the area of the sector?
- 6π cm² (Correct answer)
- 3π cm²
- 12π cm²
- 36π cm²
Correct answer: 6π cm²
Area = (θ/360°)·πr² = (60/360)·π(36) = 6π cm².
NBT Mathematics: Geometry and Trigonometry 2
A circle has a radius of 7 cm.
What is its circumference?