Chapter 16.2, Problem 1PS

To determine

To find: Thediameter of the circle circumscribed about $\Delta ABC$ .

Answer to Problem 1PS

The diameter of the circle circumscribed about $\Delta ABC$ is $6.110\text{unit}$ .

Explanation of Solution

Given information:

The given figure is,

  

The length $BC$ is calculated as,

  $\begin{array}{l}{\left(BC\right)}^2={\left(AB\right)}^2+{\left(AC\right)}^2-2\left(AC\right)\left(AB\right)\cos \left(60°\right)\\ {\left(BC\right)}^2={\left(4\right)}^2+{\left(6\right)}^2-2\left(6\right)\left(4\right)\cos \left(60°\right)\\ BC=2\sqrt{7}\text{units}\end{array}$

Calculate the diameter of the circle as,

  $\begin{array}{c}D=\frac{BC}{\sin 60°}\\ =\frac{2\sqrt{7}}{\sin 60°}\\ =6.110\text{unit}\end{array}$

Thus, the diameter of the circle circumscribed about $\Delta ABC$ is $6.110\text{unit}$ .