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In triangle PQR, let X be the intersection of the angle bisector of angle P with side QR, and let Y be the foot of the perpendicular from X to line PR.  If PQ = 9, QR = 9, and PR = 9, then compute the length of XY.

 Jun 13, 2023
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 Compute the length of XY.

 

Hello Guest!

 

\(\overline {XY}=\overline{PR}\cdot cos\ 30^{\circ}=\sqrt{\overline{PR}\ ^2-(\frac{\overline{PR}}{2})^2}\\ \overline{XY}=9\cdot cos\ 30^{\circ}=\sqrt{9^2-(\frac{9}{2})^2}=\color{blue}7.794\)

The length of  \(\overline{XY}\)  is 7.794.

laugh  !

 Jun 14, 2023

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