## Area of a Triangle using Sine

Everyone knows the formula $\frac{1}{2}$ x base x height for working out the area of a triangle. But what happens when you can’t work out the height of a triangle, what can you do then?

Luckily trigonometry has the answer, with the formula Area = $\frac{1}{2}ab\sin{C}$.

Where C is the angle between the sides a and b, (see diagram above).

Example

Find the area $A$ of the above triangle (not to scale) using the information given.

Using the above formula, we get the following equation:

$A = \frac{1}{2} \times 10 \times 7 \times \sin{52}$

So $A = 35 \sin{52} = 27.58$ to two decimal places.

Note – It does not matter which sides or angles you choose in your formula, just as long as you choose the angle enclosed by the two chosen sides.