Chapter 9, Problem 12RP

To determine

To find:The values of TV and TZ.

Answer to Problem 12RP

The values are $TV=\frac{4}{\sqrt{3}}$ and $TZ=\frac{2}{\sqrt{3}}$

Explanation of Solution

Given information:The following information has been given

  $TX=8$

  $VW=12$

  $\angle V={30}^0$

Calculation:First of all, in right triangle TZV, we have

  $VZ=\frac{VW-TX}{2}=2$

Now, we also know that $\angle V={30}^0$ . Hence, we can say

  $\begin{array}{l}\tan {30}^0=\frac{TZ}{VZ}\\ \frac{1}{\sqrt{3}}=\frac{TZ}{VZ}\\ \frac{1}{\sqrt{3}}=\frac{TZ}{2}\\ TZ=\frac{2}{\sqrt{3}}\end{array}$

And,

  $\begin{array}{l}\cos {30}^0=\frac{VZ}{TV}\\ \frac{\sqrt{3}}{2}=\frac{VZ}{TV}\\ \frac{\sqrt{3}}{2}=\frac{2}{TV}\\ TV=\frac{4}{\sqrt{3}}\end{array}$