Calculating Triangle Sides and Angles with Cosines

A triangle has sides of lengths 8 cm and 6 cm, with an included angle of 60 degrees. Calculate the length of the third side using the law of cosines.

• 2√13 cm

• 5 cm

• 7 cm

• 10 cm

In a triangle, one side measures 10 m, another side measures 14 m, and the angle between them is 45 degrees. Determine the length of the third side.

• 12.75 m

• 15.00 m

• 8.50 m

• 9.24 m

A ladder leans against a wall, forming a triangle with the ground. If the ladder is 15 ft long and the angle between the ladder and the ground is 30 degrees, how high up the wall does the ladder reach?

• 10 ft

• 5 ft

• 12 ft

• 7.5 ft

A triangle has sides of lengths 7 m and 9 m, with an included angle of 120 degrees. Calculate the length of the third side using the law of cosines.

• 13.89 m

• 15.2 m

• 12.3 m

• 10.5 m

In a triangle, two sides measure 5 cm and 12 cm, and the angle opposite the 12 cm side is 75 degrees. Find the length of the side opposite the 5 cm side.

• 10 cm

• 11.5 cm

• 9 cm

• 13 cm

A boat sails from point A to point B, then to point C, forming a triangle. If AB = 10 km, AC = 8 km, and angle A = 50 degrees, calculate the distance BC.

• 12.50 km

• 9.00 km

• 7.81 km

• 5.00 km

A triangular park has sides measuring 20 m, 25 m, and an angle of 60 degrees between the two shorter sides. Calculate the length of the longest side.

• 23.0 m

• 22.91 m

• 21.5 m

• 24.5 m

In a triangle, one side measures 13 m, another side measures 15 m, and the angle between them is 30 degrees. Determine the length of the third side using the law of cosines.

• 10.5 m

• Approximately 7.87 m

• 12.3 m

• 9.1 m

A construction worker needs to find the angle between two beams that meet at a point. If the beams are 12 ft and 16 ft long, and the distance between their endpoints is 10 ft, what is the angle between the beams?

• 43.6 degrees

• 30 degrees

• 60 degrees

• 90 degrees

A triangular field has sides of lengths 9 m, 12 m, and an angle of 45 degrees between the two shorter sides. Calculate the length of the longest side using the law of cosines.

• Approximately 8.5 m

• Approximately 12.5 m

• Approximately 9.8 m

• Approximately 10.63 m