Mastering Triangle Problems with the Law of Cosines

A surveyor is measuring a triangular plot of land. One side measures 150 meters, another side measures 200 meters, and the angle between them is 60 degrees. How long is the third side of the triangle?

• 210 meters

• 218.24 meters

• 250 meters

• 180 meters

A boat sails from point A to point B, then to point C, forming a triangle. The distance from A to B is 10 km, from B to C is 15 km, and the angle at B is 45 degrees. What is the distance from A to C?

• 5 km

• 8.66 km

• 20 km

• 12 km

In a triangle, one side measures 8 cm, another side measures 6 cm, and the angle between them is 120 degrees. Calculate the length of the third side using the law of cosines.

• 10.5 cm

• 9.8 cm

• 14.3 cm

• 12.17 cm

A triangular park has sides measuring 50 meters, 70 meters, and an angle of 45 degrees between the two known sides. Find the length of the side opposite the 45-degree angle.

• 70 meters

• Approximately 36.06 meters

• 50 meters

• 45 meters

A ladder leans against a wall, forming a triangle with the ground. The ladder is 12 feet long, and the angle between the ladder and the ground is 60 degrees. How high up the wall does the ladder reach?

• 10.392 feet

• 11.000 feet

• 9.500 feet

• 8.000 feet

A triangle has two sides measuring 5 m and 7 m, with an included angle of 30 degrees. Use the law of cosines to find the length of the third side.

• c ≈ 3.75 m

• c ≈ 6.12 m

• c ≈ 4.24 m

• c ≈ 5.50 m

A triangular garden has one side measuring 30 feet, another side measuring 40 feet, and the angle between them is 90 degrees. What is the length of the third side?

• 50 feet

• 60 feet

• 70 feet

• 45 feet

A triangle has sides of lengths 9 cm and 12 cm, with an angle of 120 degrees between them. Calculate the length of the third side using the law of cosines.

• 18.25 cm

• 20 cm

• 15.5 cm

• 12.5 cm

A cable is stretched between two poles, forming a triangle with the ground. If one pole is 10 meters tall, the other is 15 meters tall, and the distance between the bases of the poles is 20 meters, what is the length of the cable?

• 15.000 meters

• 25.000 meters

• 20.615 meters

• 18.500 meters

In a triangle, one side measures 14 m, another side measures 10 m, and the angle between them is 75 degrees. Find the length of the third side using the law of cosines.

• 14.93 m

• 13.75 m

• 16.20 m

• 12.50 m