Question

In ∆QRS, the measure of

Answer 1

Notice that the given triagle is a right triangle. Remember the definition of the cosine of an angle on a right triangle.

$\cos (\theta)=\frac{\text{Side adjacent to }\theta}{\text{ Hypotenuse}}$

Plugging in the information of the diagram:

$\cos (\angle SQR)=\frac{SQ}{QR}$

Substitute the given values of each segment:

$\cos (29)=\frac{5}{x}$

Isolate x and use a calculator to find a decimal expression for x:

$\begin{gathered} x=\frac{5}{\cos (29)} \\ \Rightarrow x=5.716770339\ldots \\ \Rightarrow x\approx5.7 \end{gathered}$

Therefore, the length of the side QR, to the nearest tenth of a foot is:

$5.7$