Answer:
The largest angle needed is [tex]95.1^{o}[/tex].
Step-by-step explanation:
To determine the larges angle as required, let us apply the cosine rule.
[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2ab Cos C
Since in triangles, the longest side is opposite to the largest angle, then;
[tex]15^{2}[/tex] = [tex]8^{2}[/tex] + [tex]12^{2}[/tex] - 2(8 x 12) Cos θ
225 = 64 + 144 - 192 Cos θ
225 = 208 - 192 Cos θ
192 Cos θ = 208 -225
192 Cos θ = -17
Cos θ = [tex]\frac{-17}{192}[/tex]
Cos θ = -0.08854
θ = [tex]Cos^{-1}[/tex] -0.08854
= 95.07962
θ = [tex]95.1^{o}[/tex]
The largest angle needed is [tex]95.1^{o}[/tex].
