Question
Given that ABC is a right triangle with A = 90, B = 25, and BC = 5 inches, which of the following correctly uses the sine ratio to find the length of AC?
Answers
GPT-4o mini
In triangle ABC, where angle A is \(90^\circ\) and angle B is \(25^\circ\), you can use the sine ratio to find the length of side AC. In this triangle, side AC is opposite to angle B.
The sine ratio is defined as:
\[
\sin(B) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
In this case:
- The opposite side to angle B (which is AC) is what we are trying to find.
- The hypotenuse of triangle ABC is side BC, which is given as 5 inches.
We can write the equation using the sine ratio:
\[
\sin(25^\circ) = \frac{AC}{BC}
\]
Substituting the known length of the hypotenuse (BC = 5 inches), we have:
\[
\sin(25^\circ) = \frac{AC}{5}
\]
To solve for AC, we rearrange the equation:
\[
AC = 5 \cdot \sin(25^\circ)
\]
Thus, this equation correctly uses the sine ratio to find the length of side AC.
The sine ratio is defined as:
\[
\sin(B) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
In this case:
- The opposite side to angle B (which is AC) is what we are trying to find.
- The hypotenuse of triangle ABC is side BC, which is given as 5 inches.
We can write the equation using the sine ratio:
\[
\sin(25^\circ) = \frac{AC}{BC}
\]
Substituting the known length of the hypotenuse (BC = 5 inches), we have:
\[
\sin(25^\circ) = \frac{AC}{5}
\]
To solve for AC, we rearrange the equation:
\[
AC = 5 \cdot \sin(25^\circ)
\]
Thus, this equation correctly uses the sine ratio to find the length of side AC.