In these lessons, we will learn how to find the area of a triangle using the sine function when given side-angle-side (SAS).

Related Topics:

More Trigonometric Lessons

More Geometry Lessons

The most common formula for the area of a triangle would be:

Area = ½ × base(b) × height (h)

Another formula that can be used to obtain the area of a triangle uses the sine function. It allows us to find the area of a triangle when we know the lengths of two sides and the size of angle between them.

The formula is

Area of triangle = ½ ab sinC

Remember that the given angle must be between the two given sides.

**Example:**

Find the area of triangle *PQR* if *p* = 6.5 cm, *r* = 4.3 cm and ∠ *Q* = 39˚. Give your answer correct to 2 decimal places.

**Solution:**

Area of triangle *PQR*

= ½ pr sinQ

= ½ × 6.5 × 4.3 × sin 39˚

= 8.79 cm^{2}

**Example:**

In triangle *ABC* if *AC* = 2*BC* and ∠ *C* = 112˚. The area of triangle *ABC* is 16.3 cm Find the length of *BC* . Give your answer correct to 2 significant figures.

**Solution:**

Let the length of *BC* = *x*

and the length of *AC* = 2*x*

*x* = 4.19 cm

So, *BC* = 4.2 cm

The Area of a Triangle using Sine

This video explains how to determine the area of a triangle using the sine function when given side-angle-side (SAS).

Example:

- Determine the area of the following triangle:

a) A = 35°, B = 82°, a = 6 cm, b = 15 cm

b) B = 72°, a = 23.7 ft, b = 35.2 ft.

**Determine the Area of a Triangle Using the Sine Function**

This video provides an example of how to determine the area of a triangle using the sine function.

**How to use the sine function to find the area of a triangle?**

Example:

Find the area of the oblique triangle with the given information

A = 100°, b = 14, c = 21

**Area Triangles using Sine**

This video explains how to find the area of a triangle using Sine.

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