Question

2 find uw.
explain your reasoning.

Explanation:

Step1: Use the Pythagorean theorem in \(\triangle TUV\)

In right - triangle \(TUV\), by the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = TU=18\) and \(b = UV\). Let \(a\) be the length of \(TV\).

$$TV=\sqrt{18^{2}-UV^{2}}$$

In right - triangle \(TWV\), \(TW = 18\) and \(WV = 7.2\). Let \(TV\) be the common leg.
Since \(T\) is on the angle bisector and \(TU = TW\), and \(TV\perp UW\), by the property of the angle bisector (if a point is on the angle bisector and two segments from the point to the sides of the angle are equal in length (here \(TU = TW\)) and perpendicular to the sides (\(TV\perp UW\)), then \(UV=WV\))

Step2: Calculate \(UW\)

Since \(UV = WV\) and \(UW=UV + WV\), given \(WV = 7.2\)

$$UW=7.2+7.2$$

Answer:

\(14.4\)