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Question

# Tell whether you should use the Law of Sines, the Law of Cosines, or the Pythagorean Theorem and trigonometric ratios to solve the triangle with the given information. Explain your reasoning. m∠C = 40°, b = 27, c = 36.

Solution

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Given the lengths of $2$ sides and the measure of non-included angle, use the $\text{Law of Sines}$

Use the formula $\frac{\sin B}{b}=\frac{\sin C}{c}$

Let

\begin{aligned}b&=27\\ c&=36\\ C&=40\degree \end{aligned}

Substitute the values of $b,c$ and $C$ in the given formula, then simplify

\begin{aligned}\frac{\sin B}{b}&=\frac{\sin C}{c}\\ \frac{\sin B}{27}&=\frac{\sin 40\degree}{36}\\ 27\left(\frac{\sin B}{27}\right)&=\left(\frac{\sin 40\degree}{36}\right)27\\ \sin B&=\left(\frac{\sin 40\degree}{36}\right)27\\ &=0.482090707 \end{aligned}

Use calculator to find $m\angle B$

\begin{aligned}m\angle B=28.8\degree \end{aligned}

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