Mathematics: Geometry and Trigonometry Flashcards

A circle has a radius of 7 cm. What is its circumference?

Answer: 14π cm

Circumference = 2πr = 2π(7) = 14π cm.

In triangle ABC, angle A = 35° and angle B = 75°. What is angle C?

Answer: 70°

Angles in a triangle sum to 180°, so C = 180° − 35° − 75° = 70°.

What is sin(45°)?

Answer: √2/2

sin(45°) = √2/2 ≈ 0.707, derived from the 45-45-90 triangle.

A rectangle has length 12 m and width 5 m. What is the length of its diagonal?

Answer: 13 m

By the Pythagorean theorem, diagonal = √(12² + 5²) = √(144 + 25) = √169 = 13 m.

The bearing of point B from point A is 120°. What is the bearing of A from B?

Answer: 300°

The reverse bearing is found by adding or subtracting 180°: 120° + 180° = 300°.

Which of the following is the correct cosine rule for triangle ABC?

Answer: a² = b² + c² − 2bc·cos A

The cosine rule states a² = b² + c² − 2bc·cos A.

A sector of a circle has radius 6 cm and central angle 60°. What is the area of the sector?

Answer: 6π cm²

Area = (θ/360°)·πr² = (60/360)·π(36) = 6π cm².