Chapter 9.7, Problem 8PSA

To determine

To calculate: The unknown segment CD.

Answer to Problem 8PSA

The unknown segment CD is $4\sqrt{3}$

Explanation of Solution

Given information :

  $\begin{array}{l}\overline{AC}\perp \overline{BC},\overline{CD}\perp \overline{AB},\overline{BC}=8\sqrt{3}\\ \angle B=30°\end{array}$

Formula used :

In $30°-60°-90°$ triangle, sides are in ratio $x:x\sqrt{3}:2x$

Calculation :

In triangle DCB, we have

BC = $8\sqrt{3}$ =2 x ….. as this is the longest side in the triangle

  $\therefore 2x=8\sqrt{3}\Rightarrow x=4\sqrt{3}$

Hence, CD is the lowest side in the triangle, will be $4\sqrt{3}$