Real-World Triangle Challenges: Law of Cosines Quiz

A surveyor is measuring a triangular plot of land. If one side is 150 meters, another side is 200 meters, and the angle between them is 60 degrees, what is the length of the third side?

• 180.28 meters

• 160 meters

• 190 meters

• 210 meters

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

• 8 km

• 20 km

• 10.5 km

• 12.36 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.

• 9.8 cm

• 12.17 cm

• 10.5 cm

• 14.3 cm

A triangular park has sides measuring 50 m, 70 m, and an angle of 45 degrees between the two known sides. What is the length of the third side of the park?

• 36.06 m

• 45.00 m

• 50.00 m

• 70.00 m

A cable is stretched between two poles that are 30 meters apart, forming a triangle with a height of 40 meters from the midpoint of the cable to the ground. What is the length of the cable?

• 100 meters

• 75 meters

• 60 meters

• 85.44 meters

A triangle has sides of lengths 12 cm and 16 cm, with an included angle of 30 degrees. Find the length of the third side using the law of cosines.

• c ≈ 14.42 cm

• c ≈ 12.50 cm

• c ≈ 18.00 cm

• c ≈ 10.00 cm

A triangular garden has one side measuring 25 feet, another side measuring 30 feet, and the angle between them is 60 degrees. What is the length of the third side?

• 25.0 feet

• 27.86 feet

• 32.1 feet

• 20.5 feet

A construction worker needs to determine the distance between two points on a triangular site. If one side is 100 m, another side is 80 m, and the angle between them is 75 degrees, what is the length of the third side?

• 75 m

• 66.57 m

• 90 m

• 85 m

In a triangle, one side is 9 m, another side is 12 m, and the angle between them is 120 degrees. Calculate the length of the third side using the law of cosines.

• 10 m

• 20 m

• 18.25 m

• 15 m

A triangular field has sides measuring 40 m, 50 m, and an angle of 60 degrees between the two known sides. What is the length of the third side of the field?

• 30 m

• 45.83 m

• 55 m

• 60 m