NBT - National Benchmark Mathematics: Geometry and Trigonometry Questions and Answers 2

Question 1

In triangle ABC, angle A = 35° and angle B = 85°. What is the size of angle C?

Accepted Answer

60°

Answer

The sum of angles in a triangle = 180°. Angle C = 180° - 35° - 85° = 60°.

Question 2

A right-angled triangle has a hypotenuse of 13 cm and one leg of 5 cm. What is the length of the other leg?

Accepted Answer

12 cm

Answer

Using Pythagoras: c² = a² + b². 13² = 5² + b². 169 = 25 + b². b² = 144. b = 12 cm.

Question 3

What is the area of a circle with radius 7 cm? (Use π ≈ 22/7)

Accepted Answer

154 cm²

Answer

Area = πr² = (22/7) × 7² = (22/7) × 49 = 22 × 7 = 154 cm².

Question 4

If sin θ = 3/5, what is the value of cos θ for 0° < θ < 90°?

Accepted Answer

4/5

Answer

Using sin²θ + cos²θ = 1: (3/5)² + cos²θ = 1. cos²θ = 1 - 9/25 = 16/25. cos θ = 4/5.

Question 5

A rectangle has length 12 cm and width 8 cm. What is the length of its diagonal?

Accepted Answer

4√(13) cm

Answer

Diagonal = √(12² + 8²) = √(144 + 64) = √208 = 4√13 cm.

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