Question

The Sine and Cosine Ratios Quick Check 1 of 51 of 5 Items 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=5sin25° upper A upper C equals 5 sine 25 degrees AC=5sin25° upper A upper C equals Start Fraction 5 over sine 25 degrees End Fraction AC=5sin65° upper A upper C equals 5 sine 65 degrees AC=5sin65° upper A upper C equals Start Fraction 5 over sine 65 degrees End Fraction Skip to navigation 1 of 1 page 21 of 21

Answer 1

In triangle \( \triangle ABC \), given that:

• \( \angle A = 90^\circ \)
• \( \angle B = 25^\circ \)
• \( BC = 5 \) inches

To find the length of \( AC \) using the sine ratio, we can use the sine definition in a right triangle, which relates the opposite side to the hypotenuse. The angle B corresponds to side AC, and the hypotenuse is BC. According to the sine ratio:

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

From this, we can set up the equation:

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

From this, we can rearrange to find \( AC \):

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

So the correct response is:

AC = 5 sin 25°