Chapter 13.1, Problem 48WE

To determine

To find: The all to three significant digits and angles.

Answer to Problem 48WE

The angles of the triangle are $A={31.8}^o$ , $B\approx {38.9}^o$ , and $C\approx 109.3^o$ .

Explanation of Solution

Given information:

The given sides of a triangle $a=5$ , $b=6$ , and $c=9$ .

Calculation:

Consider the triangle is shown below.

  

Since we do not know the any of the angle measure, we cannot use the law of sine.

Use the law of cosine.

  $c^2=a^2+b^2-ab\cos C$

Substitute the value of $a$ , $b$ and $c$ .

  $\begin{array}{c}{9}^2=5^2+6^2-2\left(5\right)\left(6\right)\cos C\\ \cos C=0.33\\ C={\cos }^{-1}\left(-0.33\right)\\ C={109.268}^o\\ C\approx {109.3}^o\end{array}$

Similarly,

  $B\approx {38.9}^o$

Thus, the third angle is:

  $\begin{array}{l}A={180}^o-\left(B+C\right)\\ A=180-\left({38.9}^o+{109.3}^o\right)\\ A={31.8}^o\end{array}$

Therefore, the angles of the triangle are $A={31.8}^o$ , $B\approx {38.9}^o$ , and $C\approx 109.3^o$ .