The triangular garden ABC A = 35degrees, c= 12 m and a = 9m find the perimeter

Question

Brett owns a landscaping business. he went to the garden supply centre to buy edging for the perimeter of a triangular garden. When he got there he realised he did not have all the measurements. The triangular garden ABC A = 35degres, c= 12 m and a = 9m find the perimeter

Answer 1

a²=b²+c²-2bccosA. We don’t know b but we can find it using the Cosine Rule:

81=b²+144-24bcos35, b²-24bcos35+63=0.

Applying the quadratic formula we get: 

b=(24cos35±√(576cos² 35-252))/2=15.63m or 4.03m.

So there are two possible answers for the perimeter depending on which value for b we use. Both are valid.

The picture shows two points C1 and C2 corresponding to the two different values for b. So the perimeter is 25.03m or 36.63m. The latter seems the more likely one.