Question

Determine each ratio as a decimal to four places, then find the angle to the nearest whole numberАAngleRatioRatio as adecimalsin c15 cm8 cmCOS CLan Btan cC С17 cmBcos BIsin B

Answer 1

Using trigonometry functions:

$\begin{gathered} \sin (C)=\frac{opposite}{hypotenuse}=\frac{8}{17}=0.4706 \\ C=\sin ^{-1}(\frac{8}{17})=28 \end{gathered}$$\begin{gathered} \cos (C)=\frac{adjacent}{hypotenuse}=\frac{15}{17}=0.8824 \\ C=\cos ^{-1}(\frac{15}{17})=28 \end{gathered}$$\begin{gathered} \tan (B)=\frac{opposite}{adjacent}=\frac{15}{8}=1.875 \\ B=\tan ^{-1}(\frac{15}{8})=62 \end{gathered}$$\begin{gathered} \tan (C)=\frac{opposite}{adjacent}=\frac{8}{15}=0.5333 \\ C=\tan ^{-1}(\frac{8}{15})=28 \end{gathered}$$\begin{gathered} \cos (B)=\frac{adjacent}{hypotenuse}=\frac{8}{17}=0.4706 \\ B=\cos ^{-1}(\frac{8}{17})=62 \end{gathered}$$\begin{gathered} \sin (B)=\frac{opposite}{hypotenuse}=\frac{15}{17}=0.8824 \\ B=\sin ^{-1}(\frac{15}{17})=62 \end{gathered}$