Question

In triangle ABC, a = 8, b = 6, and C = 60°. Find the measure of A. 16° 46° 74° 106°

Answer 1

`cos~C= (a^2+b^2-c^2)/(2ab) \Leftrightarrow (1)/(2)= (64+36-c ^(2) )/(2*48) \Rightarrow 100-c^2=48 \Rightarrow c^(2)=52 \Rightarrow \\ c=2 √(13).~~~~~(Cosinus~formula) \\ \\ cos~A= (b^2+c^2-a^2)/(2bc)= (36+52-64)/(24 √(13) ) = (24)/(24 √(13) )= ( √(13) )/(13). \\ \\ cos~A= ( √(13) )/(13) \Rightarrow m(\ \textless \ A) =74 \textdegree.`