Chapter 8.3, Problem 36AYU

To determine

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

Answer to Problem 36AYU

Solution:

$B = 29.9°, C = 65.1° \text{and} c \approx 12.75$

Explanation of Solution

Given:

$a = 14, b = 7, A = 85°$

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:

$a = 14, b = 7, A = 85°$

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

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

$\frac{\text{sin}85° }{14} = \frac{\text{sin}B}{7}$

$B \approx \frac{1}{2} * \text{sin}85°$

$B \approx 29.9°$

$C = 180° - 29.9° - 85° = 65.1°$

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

$\frac{\text{sin}29.87° }{7} = \frac{\text{sin}65.1° }{c}$

$c = 7 * \frac{\text{sin}55}{\text{sin}75}$

$c \approx 12.75$