Question
Given any triangle ABC labeled as shown, the law of sines states:
Question Blank 1 of 1
The ratio of the sine of an angle to the length of the longest side is the same for all parts of the triangle.
The ratio of the sine of an angle to the length of the adjacent side is the same for all parts of the triangle.
The ratio of the sine of an angle to the length of the shortest side is the same for all parts of the triangle.
The ratio of the sine of an angle to the length of the opposite side is the same for all parts of the triangle
Question Blank 1 of 1
The ratio of the sine of an angle to the length of the longest side is the same for all parts of the triangle.
The ratio of the sine of an angle to the length of the adjacent side is the same for all parts of the triangle.
The ratio of the sine of an angle to the length of the shortest side is the same for all parts of the triangle.
The ratio of the sine of an angle to the length of the opposite side is the same for all parts of the triangle
Answers
GPT-4o mini
The correct statement regarding the Law of Sines is:
**The ratio of the sine of an angle to the length of the opposite side is the same for all parts of the triangle.**
In mathematical terms, the Law of Sines can be expressed as:
\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]
where \( a, b, c \) are the lengths of the sides opposite to angles \( A, B, C \), respectively.
**The ratio of the sine of an angle to the length of the opposite side is the same for all parts of the triangle.**
In mathematical terms, the Law of Sines can be expressed as:
\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]
where \( a, b, c \) are the lengths of the sides opposite to angles \( A, B, C \), respectively.