Triangle Measurements and Angle Calculations

The video tutorial explains how to solve various geometric problems involving triangles and angles. It covers the use of sine and cosine rules to calculate distances and angles between cities and within triangles. The tutorial provides step-by-step solutions to find unknown sides and angles, emphasizing the application of trigonometric principles in practical scenarios.

What is the distance between cities A and B if the angle between road M and road E is 70° and the angle between road K and road M is 30°?

• 10.1 km

• 8.2 km

• 9.4 km

• 7.5 km

In triangle ABC, if angle A is 45° and angle B is 30°, what is the length of side BC given AC is 6?

• 6√2

• 5√2

• 7√2

• 8√2

Using the cosine rule, what is the length of side BC in a triangle where angle A is 60°, side AB is 6, and side AC is 4?

• √28

• 2√7

• 4√7

• 3√7

In triangle PQR, if PQ = 2, QR = 1, and PR = √7, what is the measure of angle Q?

• 45°

• 30°

• 60°

• 90°