In triangle ABC, a = 9 cm, b = 10 cm and c = 13 cm. Find the size of the largest angle.

Step 1: Recall the cosines formula
The law of cosines is a formula that relates the three sides of a triangle to
the cosine of a given angle
FORMULA: a^2 = b^2 + c^2 - 2bc \cos(A)
b^2 = a^2 + c^2 - 2ac \cos(B)
c^2 = b^2 + a^2 - 2ba \cos(C)
Where each lowercase letter (like a) is the length of the side opposite the
vertex labeled with the same capital letter.
Step 2: Determine the largest angle in the triangle
GIVEN: In a triangle ABC
a = 9 cm
b = 10 cm
c = 13 cm
The largest angle is the one facing the longest side, i.e. C.
Substitute the given lengths in the law of cosines formula.
c^2 = b^2 + a^2 - 2ab\cos (C)
13^2 = 10^2 + 9^2 - 2(9*10)\cos (C)
\cos (C) = \frac{10^2 + 9^2 - 13^2}{2(90)}
\cos C = \frac{100 + 81 - 169}{180}
\cos C = \frac{12}{180}
\cos C = 0.067
C = \cos^{-1}(0.67)
C = 86.2\degree
The largest angle in the triangle = C = 86.2\degree