Chapter 5.5, Problem 11CFU

To determine

To solve: The triangle, given the triangle at the right. Round to the nearest tenth if necessary, $B={78}^{\circ },a=41$

Answer to Problem 11CFU

  $\begin{array}{l}b=192.9,\\ c=197.2,\\ m\angle A={12}^{\circ },\\ m\angle C={90}^{\circ }\end{array}$

Explanation of Solution

Given information: Triangle:

Calculation:

Lots of ways to completely solve but often you have to start with what’s given. We have an angle and an adjacent side, so we start with either tangent or cosine

You can solve for c with either the cosine (or sine now that you know b ) or the Pythagorean Theorem.

  $\begin{array}{l}\tan {78}^{\circ }=\frac{b}{41}\\ b=4.7046\times 41\\ b=192.9\end{array}$

Should be the longest side

  $\begin{array}{l}\cos {78}^{\circ }=\frac{41}{c}\\ c=\frac{41}{\cos {78}^{\circ }}=197.2\end{array}$

  $m\angle A={90}^{\circ }-{78}^{\circ }={12}^{\circ }$

  $\begin{array}{l}b=192.9,\\ c=197.2,\\ m\angle A={12}^{\circ },\\ m\angle C={90}^{\circ }\end{array}$