Final answer:
The law of sines relates the sides and angles of a triangle. To solve for an unknown side, one can use the ratios of sides to the sines of their opposite angles. The answers must make sense in the context of the triangle's proportions.
Step-by-step explanation:
The law of sines provides a relationship between the angles and sides of a triangle, stating that the ratio of the length of a side to the sine of its opposite angle is the same for all three sides. To find an unknown side or angle, you substitute the known values into the law of sines formula.
For example, if you know two angles and one side of a triangle, you can find the missing side using the formula a/sin(A) = b/sin(B) = c/sin(C), where a, b, and c are the sides of the triangle, and A, B, and C are the opposite angles. In practical applications, ensure the angle measurements are in radians when computing trigonometric functions.
To check if the calculated side length makes sense, compare it to the known sides and angles, considering the proportions of the triangle. Additionally, considering the Pythagorean theorem can help in cases involving right triangles.