Since we are given the lengths of 2 sides with the angle in between, therefore by cosine law we can only construct 1 triangle from this. By stating the angle in between, this constricts the possible number of triangles that can be formed into 1.
By calculation, the length of the 3rd side is calculated using cosine law:
c^2 = a^2 + b^2 – 2abcosθ
c^2 = 10^2 + 8^2 – 2(10)(8)cos40
c = 6.44 cm
ANSWER:
1 triangle
