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?
a. AC = 5 sin 65*
b. AC = 5/sin25*
c. AC = 5/sin65*
d. AC = 5sin25*

Answer 1

To find the length of side AC in triangle ABC using the sine ratio, let’s analyze the triangle.

Given:
- Triangle ABC is a right triangle.
- \(\angle A = 90^\circ\)
- \(\angle B = 25^\circ\)
- Side BC (the side opposite angle A) = 5 inches.

Using the sine ratio, we know that:

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

In this case, we are interested in angle B. The side opposite angle B is AC, and the hypotenuse is BC. Therefore, we can write:

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

Substituting the known value of BC:

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

To solve for AC, we can rearrange this equation:

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

This corresponds to option **d**:

**d. AC = 5 sin 25°**

So, the correct option is **d**.