Explanation
Step 1
draw the rectangle
here we have a rigth triangle,then
Let
[tex]\begin{gathered} hypotenuse=14 \\ agle=30\text{ \degree} \\ \text{adjacent side= length= l} \end{gathered}[/tex]so, we need a function that relates those values
[tex]\cos \Theta=\frac{adjacent\text{ side}}{\text{hypotenuse}}[/tex]replace and solve for length
[tex]\begin{gathered} \cos \Theta=\frac{adjacent\text{ side}}{\text{hypotenuse}} \\ \text{hypotenuse}\cdot\cos \Theta=adjacent\text{ side} \\ 14\text{ cm }\cdot\cos 30=l \\ 12.12435\text{ cm=l} \end{gathered}[/tex]Step 2
width
similarity, we need a function that relates
[tex]\sin \text{ }\Theta=\frac{opposite\text{ side}}{\text{hypotenuse}}[/tex]let
[tex]\text{opposite side= width=w}[/tex]replace and solve for w
[tex]\begin{gathered} \sin \text{ }\Theta=\frac{opposite\text{ side}}{\text{hypotenuse}} \\ \text{hypotenuse}\cdot\sin \Theta=opposite\text{ side} \\ 14\text{ cm }\cdot\sin \text{ 30=w} \\ 7cm=w \end{gathered}[/tex]Step 3
finally, the area of a rectangle is given by
[tex]\begin{gathered} \text{Area}=\text{ length }\cdot width \\ \text{replacing} \\ \text{Area}=(12.12\cdot7)(cm^2) \\ \text{Area}=84.87(cm^2) \end{gathered}[/tex]therefore, the answer is
[tex]\text{Area}=84.87(cm^2)[/tex]I hope this helps you
