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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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Answered 2 years ago
Answered 2 years ago
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Given the lengths of 22 sides and the measure of non-included angle, use the Law of Sines\text{Law of Sines}

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

Let

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

Substitute the values of b,cb,c and CC in the given formula, then simplify

sinBb=sinCcsinB27=sin40°3627(sinB27)=(sin40°36)27sinB=(sin40°36)27=0.482090707\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 mBm\angle B

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

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