angle A = 41.0 degrees
Side AC = 9.1 yd
Side CB = 7.3 yd
Step-by-step explanation:
11) angle C = 84 degrees
andle B = 55 degrees
angle A + angle B + angle C = 180 degrees (sum of angles in a triangle)
angle A + 55 + 84 = 180
angle A + 139 = 180
angle A + 139-139 = 180 -139
angle A = 180 -139
angle A = 41 degrees
angle A = 41.0 degrees (nearest tenth)
To find side AC, we apply sine rule
c = AB = 11 yd
AC is the side opposite angle B. It is represented by b in the formula
c/sinC = b/sinB
11/sin84 = b/sin55
b = (11/sin84)(sin55)
b = 11(0.8191)/(0.9945)
b = 9.06
Side AC = b = 9.1 yd (nearest tenth)
To find side CB, we apply sine rule
a = CB
a/sinA = c/sinC
a/sin 41 = 11/sin84
a = (11/sin84)(sin 41)
a = 7.26
Side CB = a = 7.3 yd (nearest tenth)