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)=(SQ)/(QR)`

Substitute the given values of each segment:

`\cos (29)=(5)/(x)`

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

`\begin{gathered} x=(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`