Chapter 8, Problem 16RE

In Problems 8-20, find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say “No triangle."

$a=5$, $b=3$, $A={80}^{\circ }$

To determine

To find: The remaining angle(s) and side(s) of each triangle, if it (they) exists.

Answer to Problem 16RE

Solution:

$\text{c} \approx 4.56, \text{C} \approx 63.8°, \text{B} \approx 36.2°$

Explanation of Solution

Given:

$a = 5, b = 3, A = 80°$

Formula used:

$\frac{\text{sin}A}{a} = \frac{\text{sin}B}{b} = \frac{\text{sin}C}{c}$

Sum of the interior angles in a triangle is $180°$

Calculation:

$a = 5, b = 3, A = 80°$

$\frac{\text{sin}80}{5} = \frac{\text{sin}B}{3}$

$\text{sin}B = 3 * \frac{\text{sin}80}{5}$

$B = {\text{sin}}^{ -1}\left(3 * \frac{0.9848}{5}\right)$

$B = 36.2°$

$C = 180 - 80 - 36.22$

$C = 63.8°$

$\frac{\text{sin}C}{c} = \frac{\text{sin}A}{a}$

$c = 5 * \frac{0.8971}{0.9848} \approx 4.56$