### The formula

$$ \text{Area } =\frac{1}{2} \cdot c \cdot b \cdot sin(\text{A}) $$

or, in general

$$ Area = \frac{1}{2} \cdot side_1 \cdot side_2 \cdot sin(\text{included angle}) $$

Visit this url, if you want to review what is meant by 'included angle'.

#### Where does this formula come from?

**Answer**

We all know that the general formula for the area of a triangle is $$A= \frac{1}{2} \cdot base \cdot height $$.

Well, look at the picture below, the question is, *how do we get the height of the triangle?*

Well, we can use sine to solve for the side length.

$$
sin(68) = \frac{h}{8}
$$

$$
h = 8 \cdot sin(68)
$$

#### Can you identify which triangle below has an included angle?

##### Example 1

Identify two sides and the included angle!

Apply the formula!

$$ A = \frac{1}{2} \cdot c\cdot b\cdot sin(A) \\ A = \frac{1}{2} \cdot 8 \cdot 12 \cdot sin(48) \\ = 3.567 $$