Triangle Area Calculations and Sine-Cosine Problems

A triangle has two sides measuring 8 cm and 10 cm, with an included angle of 45 degrees. Calculate the area of the triangle.

• 40√2 cm²

• 20√3 cm²

• 50 cm²

• 30 cm²

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

• 45 degrees

• 25 degrees

• 38.68 degrees

• 60 degrees

A ladder leans against a wall, forming a triangle with the ground. If the ladder is 5 m long and the angle between the ladder and the ground is 60 degrees, how high does the ladder reach on the wall?

• 3.5 m

• 2.5 m

• 4.33 m

• 5.0 m

Triangle DEF has sides of lengths 7 cm, 9 cm, and 11 cm. Use the law of cosines to find the measure of the largest angle in the triangle.

• 75.4 degrees

• 90.2 degrees

• 82.8 degrees

• 78.6 degrees

A boat sails from point A to point B, then to point C, forming triangle ABC. If AB = 10 km, AC = 12 km, and angle A = 50 degrees, find the length of side BC using the law of sines.

• 7.50 km

• 9.00 km

• 10.50 km

• 8.66 km

In a triangle, the lengths of two sides are 14 m and 20 m, and the angle between them is 75 degrees. Calculate the area of the triangle.

• 100 m²

• 135.76 m²

• 150 m²

• 120 m²

A triangular park has sides measuring 50 m, 60 m, and 70 m. Use Heron's formula to find the area of the park.

• 2500 m²

• 1800 m²

• 1500 m²

• 2000 m²

A surveyor measures a triangle with sides of lengths 15 m, 20 m, and 25 m. Determine the area of the triangle using the law of cosines.

• 150 m²

• 75 m²

• 200 m²

• 100 m²

In triangle XYZ, angle X is 40 degrees, side x is 10 m, and side y is 15 m. Find angle Y using the law of sines.

• 50 degrees

• 60 degrees

• 75.5 degrees

• 90 degrees

A triangular piece of land has one angle measuring 90 degrees, and the lengths of the two other sides are 30 m and 40 m. Calculate the area of the land.

• 600 m²

• 300 m²

• 1200 m²

• 450 m²