Area Of A Triangle Using Sine

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

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

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Trigonometry