Final answer:
To find the missing angles and side length of the triangle, we can use the sum of angles in a triangle, the law of cosines, and the law of sines.
Step-by-step explanation:
To find angle B, we can use the fact that the sum of the angles in a triangle is 180 degrees. We know that angle A is 60 degrees, so the sum of angles B and C is 180 - 60 = 120 degrees. Since angles B and C are congruent (equal), we can divide 120 by 2 to find the measure of each angle. Therefore, angle B = angle C = 60 degrees.
To find side 'a', we can use the law of cosines, which states that c^2 = a^2 + b^2 - 2ab * cos(C). Plugging in the values we have, we get 9^2 = a^2 + 6^2 - 2*6*a * cos(60). Solving this equation will give us the value of 'a'.
Using the law of sines, which states that sin(A)/a = sin(B)/b = sin(C)/c, we can find the value of side 'a' by rearranging the formula as a/sin(A) = c/sin(C), and plugging in the known values. Finally, we can also find side 'b' using the same formula, rearranging it as b/sin(B) = c/sin(C).
Learn more about Triangle properties