Question

Given triangle ABC and measure of angle A=60, measure of angle C=45, AB=8, find the perimeter of triangle ABC

a) 24
b) 16
c) 22
d) 26

Answer 1

To find the perimeter of triangle ABC, use the law of sines to find the length of side BC and then sum up all three sides.

Step-by-step explanation:

To find the perimeter of triangle ABC, we need to find the length of side BC. We can use the fact that the sum of the angles in a triangle is 180 degrees to find the measure of angle B, since angle A and angle C are already given. Angle B = 180 - Angle A - Angle C = 180 - 60 - 45 = 75 degrees.

Now, we can use the law of sines to find the length of side BC. The law of sines states that the ratio of the length of a side of a triangle to the sine of the opposite angle is constant.

Let's set up the equation: sin(A) / a = sin(B) / b. Plugging in the given values: sin(60) / 8 = sin(75) / b. Solving for b, we get b = 8 * sin(75) / sin(60) = 8 * 0.9659 / 0.866 = 8.897.

The perimeter of triangle ABC is the sum of all three sides: AB + BC + AC = 8 + 8.897 + 8 = 24.897. Rounding to the nearest whole number, the perimeter of triangle ABC is approximately 25.