Question

Find C.Round to the nearest tenth.20 ft\22 ftAB18 ftC = [? ]°Law of Cosines: c2 = a2 + b2 - 2ab cos C=Enter

Answer 1

The given triangle is shown below

From the triangle

$a=22ft,b=20ft,c=18ft,C=\text{?}$

Using the law of Cosines

$c^2=a^2+b^2-2ab\cos C$

Substitute the values of a, b, c into the formula

This gives

$18^2=22^2+20^2-2(22)(20)\cos C$

Simplifying the expression

$\begin{gathered} 324=484+400-880\cos C \\ 324=884-880\cos C \end{gathered}$

Collect like terms

$\begin{gathered} 324-884=-880\cos C \\ -560=-880\cos C \end{gathered}$

Divide both sides by -880

$\begin{gathered} \frac{-560}{-880}=\cos C \\ \cos C=0.6364 \end{gathered}$

Find the value of C

$\begin{gathered} C=\cos ^{-1}(0.6364) \\ C=50.5^{\circ} \end{gathered}$