Real-Life Applications of Sines and Cosines in Triangles

A triangle has two sides measuring 8 cm and 10 cm, with an included angle of 45 degrees. Calculate the length of the third side using the law of cosines.

• c ≈ 5.00 cm

• c ≈ 7.07 cm

• c ≈ 9.50 cm

• c ≈ 10.50 cm

In triangle ABC, angle A measures 30 degrees, side a is 12 cm, and side b is 15 cm. Use the law of sines to find the measure of angle B.

• 45 degrees

• 60 degrees

• 25 degrees

• 38.68 degrees

A boat sails from point A to point B, creating a triangle with point C, where angle A is 60 degrees, side a is 5 km, and side b is 7 km. Find the distance from point B to point C using the law of sines.

• 5.5 km

• 7.5 km

• 4.8 km

• 6.2 km

A triangle has sides of lengths 7 m, 9 m, and an angle of 50 degrees opposite the 7 m side. Use the law of cosines to find the length of the third side.

• 9.75 m

• 7.05 m

• 6.50 m

• 8.25 m

In a triangle, angle A is 45 degrees, side a is 10 m, and side b is 14 m. Calculate angle B using the law of sines.

• 30 degrees

• 49.46 degrees

• 75 degrees

• 60 degrees

A ladder leans against a wall, forming a triangle with the ground. If the ladder is 15 ft long and makes a 70-degree angle with the ground, find the height the ladder reaches on the wall using the law of sines.

• 14.095 ft

• 10.8 ft

• 16.2 ft

• 12.5 ft

A triangular park has sides measuring 10 m, 14 m, and 18 m. Use the law of cosines to find the largest angle in the triangle.

• 102.45 degrees

• 78.90 degrees

• 95.74 degrees

• 85.12 degrees

In triangle XYZ, angle X is 40 degrees, side x is 8 m, and side y is 10 m. Find angle Y using the law of sines.

• 45 degrees

• 60 degrees

• 53.1 degrees

• 30 degrees

A triangular field has one angle measuring 30 degrees and two sides measuring 50 m and 70 m. Use the law of cosines to find the length of the third side.

• Approximately 45.00 m

• Approximately 36.06 m

• Approximately 50.50 m

• Approximately 60.25 m

A surveyor measures a triangle with sides of 20 m and 25 m, and an included angle of 60 degrees. Calculate the area of the triangle using the law of cosines and the formula for area.

• 125√3 m²

• 150 m²

• 200 m²

• 75√3 m²