Question

right - triangle relationships and trigonometry. what is the area of triangle abc? round to the nearest square unit. herons formula: area = \sqrt{s(s - a)(s - b)(s - c)}. 16. 8. 10

Explanation:

Step1: Calculate semi - perimeter

First, find the semi - perimeter $s$ of the triangle with side lengths $a = 16$, $b = 8$, $c = 10$. The formula for the semi - perimeter is $s=\frac{a + b + c}{2}$. So, $s=\frac{16+8 + 10}{2}=\frac{34}{2}=17$.

Step2: Apply Heron's formula

Heron's formula is $A=\sqrt{s(s - a)(s - b)(s - c)}$. Substitute $s = 17$, $a = 16$, $b = 8$, $c = 10$ into the formula:
\[

$$\begin{align*} A&=\sqrt{17(17 - 16)(17 - 8)(17 - 10)}\\ &=\sqrt{17\times1\times9\times7}\\ &=\sqrt{17\times63}\\ &=\sqrt{1071}\\ &\approx32.726 \end{align*}$$

\]
Rounding to the nearest square unit, we get 33 square units.

Answer:

33 square units