Answer: A = 33.88 degrees
B = 98.12 degrees
b = 10.66
Step-by-step explanation:
From the information given,
side a = 6
side c = 8
angle C = 48
To find angle A, we would apply the sine rule which is expressed as
a/SinA = b/SinB = c/SinC
Thus,
6/SinA = 8/Sin48
By cross multiplying,
8SinA = 6SIn48
SinA = 6SIn48/8 = 0.5574
Taking the sine inverse of 0.5574,
A = Sin^-1(0.5574)
A = 33.88 degrees
Recall, the sum of the angles in a triangle is 180 degrees. Thus,
A + B + C = 180
33.88 + B + 48 = 180
B + 81.88 = 180
B = 180 - 81.88
B = 98.12 degrees
We would find b by applying the sine rule. We have
b/sin98.12 = 8/Sin48
By cross multiplying,
bsin48 = 8sin98.12
b = 8sin98.12/sin48
b = 10.66