INFORMATION:
We have the next rhombus
And we must find the measure of
Knowing that DB = 10, BC = 13, and m∠WAD = 25°
STEP BY STEP EXPLANATION:
To find all measures, we need to use properties or the rhombus:
- DA: To find DA we need to know that all sides of the rhombus are equal. So, if BC measures 13, then DA measures 13 too.
- BW: To find BW we need to know that in a rhombus, diagonals bisect each other at right angles. That means, diagonals intersect in the middle. So, if DB = 10, then BW will be half of BD. BW = 10/2 = 5.
- WC: We can find it as one of the legs of the right triangle formed by BW, BC and WC. Where, BC is the hypotenuse.
[tex]\begin{gathered} 13^2=5^2+WC^2 \\ WC=\sqrt{13^2-5^2} \\ WC=12 \end{gathered}[/tex]
So, WC = 12.
- Angle BAC: To find this angle, we need to use that the interior triangles formed in the interior of the rhombus are congruent. So, angle BAC is congruent with the angle DAC. Then, BAC = 25°.
ANSWER:
DA = 13
BW = 5
WC = 12
BAC = 25 degrees
