The lengths of the supporting beam are 17.4 yards and 10 yards
The diagonals represents the support beams for a patio covering.
According to the diagram, the whole sides is a rhombus.
Properties of a rhombus:
- Diagonals are perpendicular bisectors
- Diagonals are angle bisectors
Let's find diagonal ME.
Using trigonometric ratios,
sin 60 = opposite / hypotenuse
sin 60 = OE / 10
OE = 10 sin 60
OE = 8.66025403784
OE = 8.7
ME = 2(8.7) = 17.4 yards
Let's find diagonal BA,
sin 30 = 0A / 10
OA = 10 sin 30
OA = 5 yards
BA = 2(5) = 10 yards
learn more rhombus here:https://brainly.com/question/15547947?referrer=searchResults