Chapter 5.6, Problem 23E

To determine

To find: The area of triangle $B={42.8}^{\circ },a=12.7,c=5.8$ . Round to the nearest tenth

Answer to Problem 23E

  $\text{Area}=25u^2$

Explanation of Solution

Given information: $B={42.8}^{\circ },a=12.7,c=5.8$

Calculation:

We have two formulas. It depends on which information we are given as to which one we use.

If we are given two sides and the included angle we use,

  $k=\frac{1}{2}bc\sin A$

If we are given (or can figure out) three angles and a side we use,

  $k=\frac{1}{2}{b}^2\frac{\sin A\times \sin C}{\sin B}$

In this problem we are given two sides and one angle, so we use the first equation,

  $\begin{array}{l}k=\frac{1}{2}ac\sin A\\ k=\frac{1}{2}\times 12.7\times 5.8\sin {42.8}^{\circ }\\ k=0.5\times 73.66\times 0.6794\\ k=25\end{array}$

Thus,

  $\text{Area}=25u^2$