Answer :
Answer: Option 4: c=13.8m, A=28.8°, B=40.1°
Explanation:
From the information given,
the known sides are a = 7.1 and b = 9.6
the known angle is C = 111.1
We would find side c by applying the cosine rule which is expressed as
c^2 = a^2 + b^2 - 2abCosC
By substituting the given values into the formula,
c^2 = 7.1^2 + 9.6^2 - 2 x 7.1 x 9.6Cos111.1
c^2 = 50.41 + 92.16 - 136.32Cos111.1
c^2 = 142.57 - 136.32Cos111.1 = 191.6448
c = √191.6448 = 13.8436
c = 13.8
To find angle A, we would apply the sine rule which is expressed as
a/SinA = c/SinC
Thus,
7.1/SinA = 13.8436/Sin 111.1
By cross multiplying, we have
13.8436SinA = 7.1Sin111.1
SinA = 7.1Sin111.1/13.8436 = 0.4785
Taking the sine inverse of 0.4785,
A = 28.8
Recall, the sum of the angles in a triangle is 180. Thus,
A + B + C = 180
28.8 + B + 111.1 = 180
139.9 + B = 180
B = 180 - 139.9
B = 40.1
Option 4: c=13.8m, A=28.8°, B=40.1°
