Chapter 16.6, Problem 4PS

To determine

To find: the height of the triangle form inside the circle having diameter $15$ .

Answer to Problem 4PS

  $h=8$ .

Explanation of Solution

Given:

Two side measure $10$ and $12$ .

Diameter of the circle is $15$ .

Concept used:

Heron’s formula:

  $A=\frac{1}{2}\times base\times height.$

  $s$ is semi perimeter:

  $s=\frac{\text{perimeter}}{2}$ .

Inradius= $\frac{A}{s}$ .

Circumradius= $\frac{abc}{4A}$ .

Calculation:

Two side measure $10$ and $12$ .

Let the third side be $c$ and altitude to this side be $h$ .

Area of the triangle $=\frac{1}{2}ch$ .

According to the given triangle is inscribed in a circle of diameter $15$ .

  $\begin{array}{l}\text{circumradius=}\frac{15}{2}=\frac{abc}{4A}.\\ \Rightarrow \frac{10\times 12\times c}{4\times \frac{1}{2}ch}=\frac{15}{2}.\\ h=8.\end{array}$

Hence, the height $h=8$ .