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:
- 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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