Question

\Using the law of sine and cosine find the measure of AB given angle A is 55, angle B is 44 an side b is 68

Answer 1

so.. .it'd be more or less like the picture below then


`\bf \textit{Law of sines} \\ \quad \\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c}\\\\ -----------------------------\\\\ \measuredangle C=180-A-B\implies \measuredangle C=180-55-44\implies \measuredangle C=81 \\\\\\ \cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c}\implies \cfrac{sin(44^o)}{68}=\cfrac{sin(81^o)}{c} \\\\\\ \overline{AB}=c=\cfrac{68\cdot sin(81^o)}{sin(44^o)}`

now, the angles are in degrees, thus, make sure your calculator is in Degree mode when taking the sines