Chapter 7, Problem 1PRE

For Exercises 1-12, solve $\Delta ABC$ subject to the given conditions, if possible. Round the lengths of the sides and the measures of the angles to 2 decimal places, if necessary.

1. a = 20, b = 29, B = 90°

To determine

To calculate the value of sides and angles of given triangle.

Answer to Problem 1PRE

  $\begin{array}{l}c=21\\ A={43.6}^o\\ C={46.4}^o\end{array}$

Explanation of Solution

Given:

  $\begin{array}{l}\angle B=90°\\ a=20\\ b=29\end{array}$

  

Apply the sin rule in the triangle ABC

  $\begin{array}{l}\frac{a}{\sin A}=\frac{b}{\sin B}\\ \sin A=\frac{a}{b}\times \sin B\\ \sin A=0.6896\\ A=43.6°\end{array}$

From triangle ABC

$\begin{array}{l}\angle C=180-(\angle A+\angle B)\\ \angle C=46.4°\end{array}$

Apply sin rule in triangle ABC

  $\begin{array}{l}\frac{c}{\sin C}=\frac{b}{\sin B}\\ c=\frac{b}{\sin B}\times \sin C\\ c=\frac{29}{\sin 90}\times \sin 46.4\\ c=21\end{array}$

Hence, the value of c=21, A=43.6^o and C=46.4^o