Answer:
A = 40 degrees
B = 60 degrees
C = 80 degrees
a = 13.1
b = 17.6
c = 20
Explanation:
They give us A = 40 degrees and B = 60 degrees and in one triangle the sum of the angles should be 180, so you add 40 and 60, and then subtract that value by 180.
40 + 60 = 100
180 - 100 = 80
C = 80 degrees
From here you use the law of sines
20/sin(80) = a/sin(40)
when you cross multiply them you should get this:
20 * sin(40) = sin(80)*a
Simplify them
12.9 = sin(80) * a
Divide them to isolate the variable
12.9/sin(80) = a
a = 13.1
To find side length b you use law of sines again
20/sin(80) = b/sin(60)
Cross multiply
20 * sin(60) = sin(80) * b
Simplify
17.3 = sin(80) * b
Divide to isolate the variable
17.3/sin(80) = b
b = 17.6