Answer:
13.75
Step-by-step explanation:
We have been given that side b = 12, c = 15 and A = 60° in triangle ABC. We are asked to find the measure of a using law of cosines.
[tex]a^2=b^2+c^2-2bc\times \text{cos}(A)[/tex], where, a, b and c are length of sides of triangle and A is opposite angle to side A.
Upon substituting our given values in above formula we will get,
[tex]a^2=12^2+15^2-2\times12\times15\times \text{cos}(60^{\circ})[/tex]
[tex]a^2=144+225-360\times \text{cos}(60^{\circ})[/tex]
[tex]a^2=369-360\times 0.5[/tex]
[tex]a^2=369-180[/tex]
[tex]a^2=189[/tex]
Now, we will take square root of both sides of our given equation.
[tex]a=\sqrt{189}[/tex]
[tex]a=13.74772708486752\approx 13.75[/tex]
Therefore, the length of a is 13.75.
