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?

AC=5/sin 65
AC=5 sin 25
AC=5 sin 65
AC=5/sin 25

Answer 1

In a right triangle, the sine of an angle is defined as the ratio of the length of the opposite side to the hypotenuse. In triangle ABC with <A=90° and <B=25°, angle C is therefore:

\[
<C = 90° - 25° = 65°
\]

Given that \(BC\) (the side opposite angle A) is \(5\) inches, we want to find the length of \(AC\) (the side opposite angle B).

We can use the sine ratio for angle B:

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

For angle B (25°):

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

So, we rearrange the formula to solve for \(AC\):

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

Given that \(BC = 5\) inches:

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

Among the options provided, the correct expression that uses the sine ratio to find the length of \(AC\) is:

\[
AC = \frac{5}{\sin 25}
\]

Therefore, the correct answer is:

**AC = 5/sin 25**.