Mastering Triangle Problem Solving with Law of Cosines

A triangle has sides of lengths 7 cm and 10 cm, with an included angle of 60 degrees. What is the length of the third side?

• 6.5 cm

• 8.89 cm

• 10.5 cm

• 9.2 cm

In a triangle, two sides measure 8 m and 15 m, and the angle between them is 45 degrees. Calculate the length of the side opposite the angle.

• c = 10 m

• c = 12 m

• c = 20 m

• c = √(289 - 120√2) m

A ladder leans against a wall, forming a triangle with the ground. If the ladder is 12 ft long and the angle between the ladder and the ground is 30 degrees, how high does the ladder reach on the wall?

• 8 ft

• 6 ft

• 4 ft

• 10 ft

A triangular park has sides measuring 5 m, 12 m, and an angle of 120 degrees between the two shorter sides. Find the length of the side opposite the 120-degree angle.

• 13.7 m

• 17.2 m

• 15.13 m

• 10.5 m

A boat sails from point A to point B, then to point C, forming a triangle. If AB = 10 km, AC = 15 km, and the angle at A is 70 degrees, how far is point C from point B?

• 8.5 km

• 15.5 km

• 10.5 km

• 12.14 km

In a triangle, the lengths of two sides are 9 cm and 14 cm, and the angle between them is 100 degrees. Determine the length of the third side.

• 20.00 cm

• 15.56 cm

• 18.75 cm

• 12.34 cm

A triangular field has one angle measuring 30 degrees and the two sides adjacent to this angle measuring 20 m and 25 m. Find the length of the side opposite the 30-degree angle.

• 15 m

• 10 m

• 18 m

• Approximately 12.25 m

A construction site is in the shape of a triangle with sides measuring 30 m, 40 m, and an angle of 60 degrees between the two shorter sides. Calculate the length of the third side.

• 32.50 m

• 36.06 m

• 45.00 m

• 40.00 m

A cable is stretched between two poles, forming a triangle with the ground. If the distance between the poles is 50 m and the angle at one pole is 45 degrees, how long is the cable?

• 60 m

• 25 m

• 35.36 m

• 40 m

A triangular garden has sides of lengths 13 ft, 14 ft, and an angle of 45 degrees between the two shorter sides. Find the length of the side opposite the 45-degree angle.

• Approximately 9.5 ft

• Approximately 10.83 ft

• Approximately 12.5 ft

• Approximately 8.2 ft