Question

In a triangle ABC, AC=24 cm, BC=30 cm, and m∠C=40°. Determine the area of the triangle. Round to nearest square centimeter.

Answer 1

The area of the triangle is 231 cm² to the nearest square centimeter

Explanation:

We can find the area of a triangle has the lengths of two sides and the measure of the included angle by using the trigonometry

A =
`(1)/(2)` × s1 × s2 × sinФ, where

• s1 and s2 are the two sides of the triangle

• Ф is the angle included between s1 and s2

In ΔABC

∵ AC = 24 cm

∴ s1 = 24

∵ BC = 30 cm

∴ s2 = 30

∵ m∠C = 40°

∴ Ф = 40°

→ By using the rule of the area above

∵ A =
`(1)/(2)` × 24 × 30 × sin(40°)

∴ A = 231.4035395 cm²

→ Round it to the nearest square centimeter

∴ A = 231 cm²

∴ The area of the triangle is 231 cm² to the nearest square centimeter