# Cosine Rule Problems

**Problem 1** In the ABC we have AB = 5cm, AC = 6cm, α = 60°. Find the length of the side BC.

Answer: √31cm.

**Problem 2** Define the type of of the triangle by it's angle, if the lengths of it's sides are:

a) 13, 14, 15;

b) 12, 35, 37;

c) 13, 15, 24.

**Problem 3** Find the size of the angle γ of the ABC, if:

a) a = 2√3cm, b = 3cm, c = √3cm;

b) a = 11cm, b = 60cm, c = 61cm.

Answer:a) - 30°;

b) - 90°.

**Problem 4** In the ABC we have AC = 3cm, BC = √5cm, α = 45°. Find the length of the side AB.

Answer:√2cm or 2√2cm.

**Problem 5** The length of the diagonale of the rectangular is 32cm, and the angle between the diagonales is 135°. Find the lengths of the sides of the rectangular.

Answer:16√2 - √2cm and 16√2 + √2cm.

**Problem 6** The center of the circumference, inscribed in a right-angled triangle, is at distance √5 and √10 from the two ends of the hypotenuse. Find the length of the hypotenuse.

Answer: 5cm.

**Problem 7** The center of the inscribed in the ABC circumference is at distance 7 and 3√3 from the points A and B. Find the length of the side AB, if the angle at the point C is 120°.

Answer: √139cm.