Law of Sines
For the triangle figure shown, what is the unknown angle in degrees?
Expand Hint
Law of Sines:
$$$\frac{a}{sin\:A}=\frac{b}{sin\:B}=\frac{c}{sin\:C}$$$
Hint 2
For oblique (non-right) triangles, use the Law of Sines to determine unknown sides/angles:
$$$\frac{a}{sin\:A}=\frac{b}{sin\:B}=\frac{c}{sin\:C}$$$
Thus, to find angle
$$B$$
with the given knowns:
$$$\frac{a}{sin\:A}=\frac{b}{sin\:B}$$$
$$$\frac{15}{sin\:25^{\circ}}=\frac{20}{sin\:B}$$$
$$$sin\:B=\frac{20\cdot sin\:25^{\circ}}{15}=0.5635$$$
$$$B=sin^{-1}(0.5635)=34.3^{\circ}$$$
34.3°
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