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 lenght of AC

AC=5/sin 25

AC=5/sin 65

AC= 5 sin 65

AC=5 sin 25

Answer 1

In a right triangle, the sine ratio is defined as:

\[
\sin(\text{angle}) = \frac{\text{opposite side}}{\text{hypotenuse}}
\]

In triangle ABC:
- \( \angle A = 90^\circ \)
- \( \angle B = 25^\circ \)
- Therefore, \( \angle C = 90^\circ - 25^\circ = 65^\circ \)

Since \( BC \) (the side opposite angle A) measures 5 inches, and we want to find the length of \( AC \) (the side opposite angle B), we can use the sine function based on angle B:

\[
\sin(B) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{AC}{BC}
\]

Rearranging gives:

\[
AC = BC \cdot \sin(B)
\]

Now, substituting the known values:

\[
AC = 5 \cdot \sin(25^\circ)
\]

Thus, the correct expression to find the length of AC using the sine ratio is:

**AC = 5 sin 25**.

Answer 2

u sure

Answer 3

Let's clarify the situation step-by-step to ensure accuracy.

1. **Triangle ABC** is a right triangle where:
- \( \angle A = 90^\circ \)
- \( \angle B = 25^\circ \)
- \( \angle C = 65^\circ \) (since the angles in a triangle sum up to \(180^\circ\))

2. **Given side**:
- \( BC = 5 \) inches, which is the side opposite \( \angle A \).

3. **Finding side AC**:
- \( AC \) is the side opposite \( \angle B \), so we can use the sine ratio based on angle \( B \):

\[
\sin(B) = \frac{\text{opposite}}{\text{hypotenuse}}
\]

Utilizing this definition, we can express it as follows:

\[
\sin(25^\circ) = \frac{AC}{BC}
\]
Rearranging this gives:

\[
AC = BC \cdot \sin(25^\circ) = 5 \cdot \sin(25^\circ)
\]

4. **Final form**: Therefore, the correct option in your original list for finding the length of AC is indeed:

**AC = 5 sin 25**

So yes, I confirm that the previous response is correct. If you require further explanation or have more questions, feel free to ask!