Chapter 12.2, Problem 21WE

To determine

To find: the value of $h\text{ and }l$ .

Answer to Problem 21WE

The value is $h=8\text{ and }l=\sqrt{73}$ .

Explanation of Solution

Given information:

The figure provided in the question,

  

  $AM=9\text{ and }VA=10$

Calculation: to find the $h\text{ and }l$ ,

Since $AM=9$ ,

  $\begin{array}{l}\frac{\sqrt{3}}{2}a=9\\ a=\frac{18}{\sqrt{3}}\text{ [multiply]}\\ a=6\sqrt{3}\text{ [simplify]}\end{array}$

Now, since $VA=10$ ,

  $\begin{array}{l}l=\sqrt{{\left(10\right)}^2-{\left(\frac{6\sqrt{3}}{2}\right)}^2}\\ l=\sqrt{100-27}\text{ [square]}\\ l=\sqrt{73}\text{ [subtract]}\end{array}$

Now, to find the height,

  $\begin{array}{l}{h}^2+{\left(3\right)}^2={\left(\sqrt{73}\right)}^2\\ h^2=73-9\text{ [sqaure and subtract]}\\ h^2=64\text{ [subtract]}\\ h=8\text{ [square root]}\end{array}$