Question

Given b = 12, c = 15 and A = 60° in triangle ABC, use the Law of Cosines to solve for a. Fill in the blank(s) to complete each step. If applicable, be sure to enter all decimal numbers with a zero in the ones place. Round your final answer to the nearest hundredth.

Answer 1

A^2 = b^2 + c^2 -2bc * cos(A)
a^2 = 144 + 225 -360 * .5
a^2 = 189
a = 13.748

Answer 2

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.