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

Question

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!