Question

given that triange ABC is a right triangle with angle A=90 degrees, angle B=25 degrees, line BC=5 inches, what is the correct sine ratio to fine the length of line AC

Answer 1

In triangle ABC, where angle A is a right angle (90 degrees) and angle B is 25 degrees, we can use the sine ratio to find the length of line AC.

Recall that the sine function is defined as:

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

In triangle ABC:

- The side opposite angle B (25 degrees) is AC.
- The hypotenuse of triangle ABC is BC, which measures 5 inches.

Using the sine function for angle B:

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

Substituting BC:

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

To solve for AC, rearrange the equation:

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

Now, compute AC using the sine of 25 degrees.

Using a calculator:

\[
\sin(25^\circ) \approx 0.4226
\]

Thus,

\[
AC \approx 5 \cdot 0.4226 \approx 2.113
\]

Therefore, the length of line AC is approximately 2.113 inches.