Chapter 16.1, Problem 5MRE

To determine

To find: the area of the given triangle.

Answer to Problem 5MRE

Area of the given triangle is26.4 square units.

Explanation of Solution

Given information:

Given lengths to three significant digits and angle measures to the nearest tenth of a degree.

  $a=7,b=10,\angle c=49°$

Calculation:

Summarize the information in a figure.

  

Since two sides and the included angle are known, the triangle is as an SAS triangle.

Use the following formula to find area of the triangle.

  $A=\frac{1}{2}ab\sin C$

Substitute 10 for $b$ , 7 for $a$ and $49°$ for $C$ , and simplify

  $\begin{array}{c}A=\frac{1}{2}ab\sin C\\ =\frac{1}{2}\left(7\right)\left(10\right)\sin 49°\\ =35\times 0.7547\\ \approx 26.4\end{array}$

Therefore, area of given triangle is 26.4 square units.