Chapter 13.4, Problem 55SR

To determine

To calculate : Using cosine formula to solve the given triangle.

Answer to Problem 55SR

  $b=21.0158or3.85425$

Explanation of Solution

Given information: $\Delta ABC$ is given in which $a=12,A={34}^{\circ },C={15}^{\circ }.$

Formula used: in $\Delta ABC$ , by cosine formula, $\cos A=\frac{b^2+c^2-a^2}{2bc}$

Calculation:

  $\begin{array}{l}putvaluesofa,AandCintheformula,\\ \cos {34}^{\circ }=\frac{b^2+225-144}{2b\times 15}\\ \therefore 0.829\times 30b=b^2+81.\\ \therefore b^2-24.87b+81=0.\\ solvingbyquadraticformula,\\ b=\frac{24.87\pm \sqrt{618.5169-324}}{2}\\ b=\frac{24.87\pm \sqrt{294.5169}}{2}\\ b=\frac{24.87\pm 17.1615}{2}\\ b=21.0158or3.85425\end{array}$