Respuesta :
line segment AB = √3 inches (option B)
Explanation:BD = 2 inches
AB = CD (opposite sides of a rectangle are equal)
To get AB, we would apply trigonometry ratio SOHCAHTOA
SInce we are looking for AB, there is no angle opposite AB. But there is angle opposite CD (its equal length)
The angle = 60 degrees
opposite = side opposite the angle = CD
hypotenuse = BD = 2
We would use sine ratio (SOH):
[tex]\sin 60=\frac{opposite}{\text{hypotenuse}}[/tex][tex]\begin{gathered} \sin \text{ 60 = }\frac{CD}{2} \\ 2(\sin \text{ 60) = CD} \\ \end{gathered}[/tex][tex]\begin{gathered} \sin \text{ 60 in root form = }\frac{\sqrt[]{3}}{2} \\ 2(\frac{\sqrt[]{3}}{2})\text{ = CD} \\ CD\text{ = }\sqrt[]{3} \end{gathered}[/tex]Recall CD = AB
line segment AB = √3 inches (option B)
