Question

the measure of angle a is 15°, and the length of side bc is 8. what are the lengths of the other two sides, rounded to the nearest tenth? ab = blank ac = blank

Explanation:

Step1: Use tangent function for AC

We know that $\tan(A)=\frac{BC}{AC}$. Given $A = 15^{\circ}$ and $BC = 8$. So $AC=\frac{BC}{\tan(A)}=\frac{8}{\tan(15^{\circ})}$.
Since $\tan(15^{\circ})=2 - \sqrt{3}\approx2 - 1.732 = 0.268$, then $AC=\frac{8}{0.268}\approx29.9$.

Step2: Use sine function for AB

We know that $\sin(A)=\frac{BC}{AB}$. So $AB=\frac{BC}{\sin(A)}$. Given $A = 15^{\circ}$ and $BC = 8$.
Since $\sin(15^{\circ})=\frac{\sqrt{6}-\sqrt{2}}{4}\approx\frac{2.449 - 1.414}{4}=\frac{1.035}{4}=0.259$, then $AB=\frac{8}{0.259}\approx30.9$.

Answer:

$AB\approx30.9$, $AC\approx29.9$