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 Start Fraction 5 over sine 25 degrees End Fraction

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=5sin65°

Answer 1

In triangle \( ABC \) with \( \angle A = 90^\circ \) and \( \angle B = 25^\circ \), side \( BC \) is the hypotenuse. We need to find the length of side \( AC \), which is opposite angle \( B \).

The sine ratio is defined as:

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

For angle \( B \), the opposite side is \( AC \) and the hypotenuse is \( BC \).

Using the sine ratio, we have:

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

Since \( BC = 5 \) inches, we can write:

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

To solve for \( AC \), we multiply both sides by 5:

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

Therefore, the correct response is:

**AC = 5 sin 25°**.