Chapter 11.2, Problem 4E

To determine

To Find: The area and three heights of the triangle each correct to three significant digits.

Answer to Problem 4E

  $\begin{array}{l}Area=109.982squnits\\ heights:16.664,13.748,12.932\end{array}$

Explanation of Solution

Given: The length of the sides of a triangle are given.

  $15,16,17$

Given: $15,16,17$

i.e.

  $a=15,b=16,c=17$

Using Heron’s formula

  $\begin{array}{l}s=\frac{1}{2}(a+b+c)\\ s=\frac{1}{2}(15+16+17)\\ s=24\\ now\\ A=\sqrt{s(s-a)(s-b)(s-c)}\\ A=\sqrt{24(24-15)(24-16)(24-17)}\\ A=\sqrt{24(9)(8)(7)}\\ A=24\sqrt{21}\\ A=109.982\\ i.e.\\ h_1=\frac{2A}{b_1}=\frac{2A}{a}=\frac{2(109.982)}{15}=16.664\\ h_2=\frac{2A}{b_2}=\frac{2A}{b}=\frac{2(109.982)}{16}=13.748\\ h_3=\frac{2A}{b_3}=\frac{2A}{c}=\frac{2(109.982)}{17}=12.932\end{array}$

Hence,

  $\begin{array}{l}Area=109.982squnits\\ heights:16.664,13.748,12.932\end{array}$