In △ABC,a=13, b=14, and c=18. Find m∠A.

Accepted Solution

Answer:m∠A = 45.86°Step-by-step explanation:A rough sketch of the triangle is shown in the attached pic.When 3 sides are given and we want to solve for an angle, we use the Cosine Rule. Which is:[tex]p^2=a^2 +b^2 -2abCosP[/tex]Where a, b, p are the lengths of 3 sides (with p being the side opposite of the angle we are solving for) and P is the angel we want to solve forThus, we have:[tex]p^2=a^2 +b^2 -2abCosP\\13^2=14^2 +18^2-2(14)(18)CosA\\169=520-504CosA\\504CosA=351\\CosA=\frac{351}{504}\\CosA=0.6964\\A=Cos^{-1}(0.6964)=45.86[/tex]