Question

question 1 of 25 given any triangle abc labeled as shown, the law of sines states that: a. the ratio of the sine of an angle to the length of the shortest side is the same for all parts of the triangle. b. the ratio of the sine of an angle to the length of an adjacent side is the same for all parts of the triangle. c. the ratio of the sine of an angle to the length of the longest side is the same for all parts of the triangle. d. the ratio of the sine of an angle to the length of the opposite side is the same for all parts of the triangle.

Explanation:

The Law of Sines formula is \(\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}\), where \(A\), \(B\), \(C\) are angles of the triangle and \(a\), \(b\), \(c\) are the lengths of the sides opposite to angles \(A\), \(B\), \(C\) respectively. This means the ratio of the sine of an angle to the length of the opposite side is the same for all parts of the triangle.

Answer:

D. The ratio of the sine of an angle to the length of the opposite side is the same for all parts of the triangle.