In the triangle below, 1) find the length of bc 2) find the are area of δ abc

1. Since we have 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:






We can conclude that the length of the side BC is .

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.

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