1. Since we have <span>two sides (AC and AB) and the included angle (60°), we are going to use the law of cosines to find the length of BC:
</span>
<span>
We can conclude that the length of the side BC is </span>
.
2. To find the area of triangle ABC we are going to use Heron's formula:
where
is the area of the triangle
is the semi-perimeter of the triangle
But first, we are going to find the semi-perimeter of our triangle using the formula:
We can infer for our triangle and from our previous calculation that
,
, and
. Lets replace those values to find the semi-perimeter of our triangle:
Finally, we can use Heron's formula to find the area of our triangle:
We can conclude that the area of our triangle is
10.42 square units.