Chapter 12, Problem 14CR

To determine

Find the measure of largest angle for triangle ABC such that $a=6,b=10\text{ and }c=7$ .

Answer to Problem 14CR

The largest angle is $100.3°$ , so option (b) is correct.

Explanation of Solution

Given information: The given triangle ABC has $a=6,b=10\text{ and }c=7$ .

Calculation: Since the given triangle ABC has $a=6,b=10\text{ and }c=7$ . And the angle opposite to largest side will be largest. Therefore with the help of cosine formula for angle $\left(\angle B\right)$ because largest side is $\left(b=10\right)$ , the largest angle is evaluated as,

  $\begin{array}{c}\cos B=\frac{a^2+c^2-b^2}{2ab}\\ \cos B=\frac{{\left(6\right)}^2+{\left(7\right)}^2-{\left(10\right)}^2}{\left(2\right)\left(6\right)\left(7\right)}\mathrm{....}\left\{\begin{array}{l}a=6,b=10\\ \text{and }c=7\end{array}\right\}\\ B={\cos }^{-1}\left(-\frac{5}{28}\right)\\ B=100.3°\end{array}$

Hence the largest angle is $100.3°$ , so option (b) is correct.