Answer:
109°
Explanation:
The Law of Cosines is good for finding angles when you know three sides. It tells you ...
a^2 = b^2 + c^2 -2bc·cos(A)
where a, b, c are the side lengths and A, B, C are the opposite angles. Here, we want a=18, since the longest side is opposite the largest angle.
Solving for cos(A), we get ...
(b^2 +c^2 -a^2)/(2bc) = cos(A)
A = arccos((b^2 +c^2 -a^2)/(2bc)) = arccos((10^2 +12^2 -18^2)/(2·10·12))
= arccos(-80/240) = arccos(-1/3) ≈ 109.471°
The largest angle of the triangle is about 109°.