Question

The figure represents the side view of a rectangular frame for metal shelves. Two diagonal bracessupport the frame.8 ft2 ftWhich is closest to the measure of x?7°14°28°76

Answer 1

AD=BC=8 ft

AB=CD=2 ft

Then,

`\begin{gathered} AC=BD=\sqrt[]{2^2+8^2} \\ =\sqrt[]{68} \\ OA=OB=OC=OD=\frac{\sqrt[]{68}}{2}\text{ ft} \end{gathered}`

In triangle BDC,

`\begin{gathered} \tan \angle BDC=(8)/(2) \\ =4 \\ \angle BDC=75.963 \\ \angle DBC=14.04 \end{gathered}`
`\begin{gathered} OE=(8)/(2) \\ =4\text{ ft} \\ \angle BDC=\angle OCD=75.96 \end{gathered}`

In triangle ODC,

`\begin{gathered} \angle ODC+\angle OCD+\angle OCD=180 \\ \\ \angle\text{DOC}=180-(2\cdot75.96) \\ \angle DOC=28 \\ \angle X=\angle DOC=28 \end{gathered}`

So, the correct option is option C.