Notice that the given triagle is a right triangle. Remember the definition of the cosine of an angle on a right triangle.
[tex]\cos (\theta)=\frac{\text{Side adjacent to }\theta}{\text{ Hypotenuse}}[/tex]
Plugging in the information of the diagram:
[tex]\cos (\angle SQR)=\frac{SQ}{QR}[/tex]
Substitute the given values of each segment:
[tex]\cos (29)=\frac{5}{x}[/tex]
Isolate x and use a calculator to find a decimal expression for x:
[tex]\begin{gathered} x=\frac{5}{\cos (29)} \\ \Rightarrow x=5.716770339\ldots \\ \Rightarrow x\approx5.7 \end{gathered}[/tex]
Therefore, the length of the side QR, to the nearest tenth of a foot is:
[tex]5.7[/tex]
