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¯¯¯¯¯¯¯¯?(1 point)
Responses

AC=5sin65°
upper A upper C equals Start Fraction 5 over sine 65 degrees End Fraction

AC=5sin25°
upper A upper C equals 5 sine 25 degrees

AC=5sin25°
upper A upper C equals Start Fraction 5 over sine 25 degrees End Fraction

AC=5sin65°

Answer 1

To find the length of \( AC \) using the sine ratio, we start by recalling the definition of the sine function in the context of right triangles. The sine of an angle is the ratio of the length of the opposite side to the hypotenuse.

In triangle \( ABC \):

- \( \angle A = 90^\circ \)
- \( \angle B = 25^\circ \)
- \( \angle C = 65^\circ \) (since \( 90^\circ + 25^\circ + C = 180^\circ \))

We know that \( BC \) is the hypotenuse, which is given as 5 inches. We want to find \( AC \), which is opposite to angle \( B \).

The sine function for angle \( B \) is:
\[
\sin(B) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{AC}{BC}
\]

So we can rewrite this as:
\[
\sin(25^\circ) = \frac{AC}{5}
\]

From this equation, we can isolate \( AC \):
\[
AC = 5 \sin(25^\circ)
\]

Now we can check the given options. The correct formulation to find \( AC \) using the sine ratio is:
\[
AC = 5 \sin(25^\circ)
\]

Therefore, the correct response is:
**AC = 5 sin 25°**.