Question

The diagonal of rectangle ABCD measures 2 inches inlength.What is the length of line segment AB?1 inchB.C60°03 inchesO4 inchesO 4/3 inches230°DUnmark this questionSave and ExitNextSubmit

Answer 1

line segment AB = √3 inches (option B)

Step-by-step 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):

`\sin 60=\frac{opposite}{\text{hypotenuse}}`
`\begin{gathered} \sin \text{ 60 = }(CD)/(2) \\ 2(\sin \text{ 60) = CD} \\ \end{gathered}`
`\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}`

Recall CD = AB

line segment AB = √3 inches (option B)