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°
upper A upper C equals 5 sine 65 degrees

1 answer

In triangle \( ABC \) with \( \angle A = 90^\circ \) and \( \angle B = 25^\circ \), we can find the length of side \( AC \) using the sine ratio. The sine ratio states that:

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

Here, \( \angle B = 25^\circ \). The side opposite \( \angle B \) is \( AC \), and the hypotenuse \( BC \) is given as 5 inches.

From the sine definition for angle \( B \):

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

Substituting the hypotenuse:

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

To solve for \( AC \):

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

Thus, the corresponding choices you provided would be:

  • AC = 5 sin 25° \[ upper A upper C equals 5 sine 25 degrees \]

This option is correct and uses the sine ratio appropriately to find the length of \( AC \).