Question

question 16 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 longest side is the same for all parts of the triangle. b. the ratio of the sine of an angle to the length of the opposite side is the same for all parts of the triangle. c. the ratio of the sine of an angle to the length of an adjacent side is the same for all parts of the triangle. d. the ratio of the sine of an angle to the length of the shortest side is the same for all parts of the triangle.

Explanation:

Step1: Recall law of sines

For a triangle \(ABC\) with sides \(a\), \(b\), \(c\) opposite to angles \(A\), \(B\), \(C\) respectively, \(\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}\).

Step2: Analyze options

Option B correctly states the law of sines as the ratio of sine of an angle to the length of its opposite - side is constant for all angles and sides in a triangle.

Answer:

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