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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 =

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 = ab sin C

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

= pr sin Q

= 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).


 
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.
The following video shows how to use the sine function to find the area of a triangle.


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

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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