Area of a triangle

Area = ____ ab sin C Fill in the blank with the correct value.

• 1/2

• 2

• ab

• sin C

XY is 8cm, XZ is 10cm, angle YXZ = 79°. Calculate the area of the triangle XYZ. Use the formula: Area = (a × b × sin C) / 2.

• 39.26 cm²

• 27.45 cm²

• 56.12 cm²

• 32.80 cm²

A national park is in the form of a triangle, ABC. Side length AB is 49 km and side length BC is 66 km. Angle ABC is 58°. What is the side length AC in km?

• 54.2 km

• 62.8 km

• 71.5 km

• 47.3 km

The triangle on the right has area 15 cm². Find the acute angle marked x. (Use Area = 1/2 ab sin C, with Area = 15, a = 5, b = 8)

• x = 48.6°

• x = 30.0°

• x = 60.0°

• x = 75.0°

For the triangle shown in the diagram: Find the size of angle Ĉ.

• 30°

• 45°

• 60°

• 90°

For the triangle shown in the diagram: Find the area of the triangle.

• 12 square units

• 18 square units

• 24 square units

• 36 square units

In triangle XYZ, XY = 10 cm, YZ = 6 cm, and the area of the triangle is 24 cm². Find sin(∠XYZ).

• 0.6

• 0.8

• 0.4

• 1.0

In triangle ABC, ∠A = 35°, ∠C = 65°, and BC = 14 cm. Using the sine rule, find the length of AC.

• 14sin 35°/sin 80° cm

• 14sin 65°/sin 80° cm

• 14sin 80°/sin 35° cm

• 14sin 80°/sin 65° cm

In triangle ABC, the area is 30 cm², AC = 10 cm, and BC = 8 cm. Find the value of ∠ACB.

• sin⁻¹(0.75)

• sin⁻¹(0.5)

• sin⁻¹(0.25)

• sin⁻¹(1.0)

In triangle GHI, GH = 9 cm, HI = 12 cm, and the area is 36 cm². Find the value of ∠GHI.

• sin⁻¹(0.5)

• sin⁻¹(0.6)

• sin⁻¹(0.8)

• sin⁻¹(0.75)