Chapter 10.8, Problem 12PSB

To determine

Find length of side PQ.

Answer to Problem 12PSB

  $PQ=4$

Explanation of Solution

Given information:

  

Calculation:

Consider the figure,

  

Apply distance formula,

  $\begin{array}{l}PR=\sqrt{{\left(9-\left(-6\right)\right)}^2+{\left(20-0\right)}^2}\\ =\sqrt{625}\\ =25\\ PS=\sqrt{{\left(4-\left(-6\right)\right)}^2+{\left(0-0\right)}^2}\\ =\sqrt{100}\\ =10\\ {\left(PS\right)}^2=PQ\cdot PR\left[\tan gent\sec antpowerTheorem\right]\\ PQ=\frac{{\left(PS\right)}^2}{PR}=\frac{{10}^2}{25}\\ PQ=\frac{100}{25}\\ PQ=4\end{array}$

Hence, $PQ=4$ .