Calculating Triangle Side Lengths with Law of 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

• 10 cm

• 7 cm

• 5 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.

• c = 8 m

• c = 12 m

• c = 10 m

• c = √(296 - 140√2) ≈ 6.83 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 far is the base of the ladder from the wall?

• 12.99 ft

• 14.5 ft

• 10 ft

• 9 ft

A triangular park has two sides measuring 12 m and 9 m, with an included angle of 75 degrees. Find the length of the third side of the park.

• 15.20 m

• 12.95 m

• 10.50 m

• 8.75 m

In a triangle, the lengths of two sides are 7 m and 24 m, and the angle opposite the 7 m side is 60 degrees. Calculate the length of the side opposite the 24 m side.

• 30.5 m

• 21.4 m

• 15.2 m

• 18.7 m

A boat sails from point A to point B, then to point C, forming a triangle. If AB = 5 km, AC = 7 km, and angle A = 50 degrees, find the distance BC using the law of cosines.

• 6.12 km

• 4.75 km

• 7.25 km

• 5.39 km

A triangle has sides of lengths 5 cm, 12 cm, and an angle of 90 degrees between them. Calculate the length of the third side using the law of cosines.

• 10 cm

• 15 cm

• 12 cm

• 13 cm

In a construction project, two beams form a triangle with lengths of 8 ft and 15 ft, and the angle between them is 40 degrees. Determine the length of the third beam.

• 14.3 ft

• 10.5 ft

• 9.8 ft

• 12.21 ft

A triangular field has sides measuring 10 m, 14 m, and an angle of 70 degrees between the two shorter sides. Calculate the length of the longest side.

• 18.3 m

• 15.24 m

• 12.5 m

• 14.7 m

A surveyor measures a triangle with sides of lengths 20 m and 25 m, and the angle between them is 30 degrees. Find the length of the third side using the law of cosines.

• c ≈ 10.0 m

• c ≈ 20.0 m

• c ≈ 25.0 m

• c ≈ 15.0 m