Area Of A Triangle Using Sine

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.
   

• Show Step-by-step Solutions

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.

• Show Step-by-step Solutions

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

• Show Step-by-step Solutions

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

• Show Step-by-step Solutions

Check out our most popular games!
Fraction Concoction	Fact Family Game	Number Bond Garden
Online Addition Subtraction Game	Penguin Solitaire	Sawayama Solitaire
Ark Solitaire	Eldritch Invasion	Shenzhen Solitaire

Check out more Solitaire games here.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.