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

AC=5sin65°
upper A upper C equals 5 sine 65 degrees

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

AC=5sin25°

Answer 1

In triangle \( \triangle ABC \), where \( \angle A = 90^\circ \) and \( \angle B = 25^\circ \), we need to use the sine ratio to find the length of \( AC \).

Since \( AC \) is opposite to angle \( B \) and we have the length of the hypotenuse \( BC = 5 \) inches, we can use the sine ratio, which is defined as:

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

In this case, the sine of angle \( B \) can be expressed as:

\[
\sin(25^\circ) = \frac{AC}{BC}
\]

Substituting \( BC = 5 \), we get:

\[
\sin(25^\circ) = \frac{AC}{5}
\]

To solve for \( AC \), we rearrange the equation:

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

Thus, the correct response is:

**AC = 5 sin 25°**.