# Area Of A Triangle Using Sine

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 cm2

Example:

In triangle ABC if AC = 2BC 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 = 2x x = 4.19 cm

So, BC = 4.2 cm

### Videos

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:

1. 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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