# How to Find the Area of a Triangle Using Trigonometry

## Finding the Area of a Using Trigonometry

The area of a triangle is found using the formula:

In this formula, **a** and **b** are lengths of two sides of the triangle and **C** is the angle between them. **sin C** means finding the sine of the angle **C**. (**sin** is the sine function, which is a trigonometric function).

The image below shows what we mean by the two sides and the angle between them:

You can use other versions of the formula to find the area:

½ bc sin A

½ ca sin B

## How to Find the Area of a Triangle Using Trigonometry

Finding the area of a triangle using trigonometry is easy.

### Question

What is the area of a triangle with sides of 6 cm and 8 cm with an angle of 30° between them, as shown below?

### Step-by-Step:

# 1

Start with the formula:

Area = ½ ab sin C

**Don't forget:** ½ ab sin C = ½ × a × b × sin C

# 2

Substitute the length of the sides and the angle between them into the formula. In our example, a = 6, b = 8 and C = 30°.

Area = ½ × 6 × 8 × sin(30°)

Area = ½ × 6 × 8 × 0.5

Area = 12 cm^{2}

**Don't forget:** ½ × a number = 0.5 × a number = a number ÷ 2.

### Answer:

The area of the triangle with with sides of 6 cm and 8 cm with an angle of 30° between them is 12 cm^{2}.