Question

I need help I don’t understand this question. DC=8.5, DW=6.

Answer 1

Recall that the diagonals of a square bisect each other, therefore:

`BW=DW=6.`

The diagonals are congruent, therefore:

`AC\cong DB=2DW=2(6)=12.`

To compute DA we use the fact that the figure is a square:

`DA=DC=8.5.`

Now, we know that the angles at the vertices are right angles, therefore:

`m\angle ABC=90.`

To determine the measure of angles ABD, and DCA we use the trigonometric function sine:

`\begin{gathered} sin(\angle ABD)=(DA)/(DB)=(√(287))/(2(12)), \\ sin(\angle DCA)=(DA)/(CA)=(√(287))/(2(12)). \end{gathered}`

Therefore:

`m\angle ABD=m\angle DCA\approx45^(\circ).`

Finally, to determine the measure of angle DWA, we use the fact that the figure is a square, therefore the diagonals bisect each other at 90° angles.

Answer:

`\begin{gathered} BW=6, \\ AC=12, \\ DA=8.5, \\ m\angle DWA=90^(\circ), \\ m\angle ABC=90^(\circ), \\ m\angle ABD=45^(\circ), \\ m\angle DCA=45^(\circ). \end{gathered}`