Question

Find C.Round to the nearest tenth.с17 ft8 ftA16 ftB В.C = [?]o

Answer 1

Let's begin by identifying key information given to us:

`\begin{gathered} AC=b=8ft \\ AB=c=16ft \\ BC=a=17ft \\ \angle C=? \end{gathered}`

To obtain the angle C, we will use the Law of Cosines as shown below:

`\begin{gathered} c^2=a^2+b^2-2ab\cdot cosC \\ We\text{ will make ''C'' the subject of the formula, we have:} \\ 2ab\cdot cosC=a^2+b^2-c^2 \\ cosC=(a^2+b^2-c^2)/(2ab) \\ a=8ft,b=16ft,c=17ft \\ cosC=(16^2+8^2-17^2)/(2*8*16)=(256+64-289)/(256)=(31)/(256) \\ cosC=0.121 \\ C=cos^(-1)(0.121)=83.05\approx83.1 \\ C=83.1^(\circ) \\ \\ \therefore C=83.1^(\circ) \end{gathered}`