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 Start Fraction 5 over sine 25 degrees End Fraction

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

AC=5sin65°

Answer 1

In a right triangle, the sine ratio is defined as the ratio of the length of the opposite side to the length of the hypotenuse. In triangle ABC, with angle A being 90° and angle B being 25°, angle C must be 65° (since the angles in a triangle sum to 180°).

Given that BC (the hypotenuse) is 5 inches and we want to find the length of AC (the side opposite angle B), we can use the sine ratio of angle B:

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

Substituting the known values:

\[
\sin(25°) = \frac{AC}{5}
\]

To find AC, we rearrange the equation:

\[
AC = 5 \sin(25°)
\]

This means the correct expression that uses the sine ratio to find the length of AC is:

**AC = 5 sin(25°)**

So the correct response is:

**AC=5sin25°**