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.
\(a^2=b^2+c^2-2bc\times \text{cos}(A)\), 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,
\(a^2=12^2+15^2-2\times12\times15\times \text{cos}(60^{\circ})\)
\(a^2=144+225-360\times \text{cos}(60^{\circ})\)
\(a^2=369-360\times 0.5\)
\(a^2=369-180\)
\(a^2=189\)
Now, we will take square root of both sides of our given equation.
\(a=\sqrt{189}\)
\(a=13.74772708486752\approx 13.75\)
Therefore, the length of a is 13.75.
