Chapter 8.3, Problem 11AYU

In Problems 9-16, solve each triangle.

To determine

To find: The remaining angle(s) and side(s) of the given triangle.

Answer to Problem 11AYU

Solution:

$\text{c} \approx 3.75, \text{B} \approx 32.1°$ and $\text{A} \approx 52.9°$

Explanation of Solution

Given:

Formula used:

$c² = a² + b² - 2ab\text{cos}C$

$b² = a² + c² - 2ac\text{cos}B$

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

Calculation:

$a = 2, b = 3 \text{and} C = 95°$

$c² = a² + b² - 2ab\text{cos}C$

$c² = 2² + 3² - 2 * 2 * 3\text{cos}95°$

$c = \sqrt{13 - 12\text{cos}95° }$

$c \approx 3.75$

$b² = a² + c² - 2ac\text{cos}B$

$\text{cos}B = \frac{a^2 + c² - b²}{2ac}$

$\text{cos}B = \frac{3² + 3.75² - 2²}{2\left(3.75\right)\left(3\right)}$

$B = {\text{cos}}^{ - 1}\left(0.8742\right) \approx 32.09°$

$A + B + C = 180°$

$A = 180° - 32.09° - 95°$

$A \approx 52.9°$