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)ResponsesAC=5sin65°upper A upper C equals Start Fraction 5 over sine 65 degrees End FractionAC=5sin65°upper A upper C equals 5 sine 65 degreesAC=5sin25°upper A upper C equals 5 sine 25 degreesAC=5sin25°upper A upper C equals Start Fraction 5 over sine 25 degrees End Fraction
Answers
GPT-4o mini
In triangle \( ABC \), since it is a right triangle with \( \angle A = 90° \), \( \angle B = 25° \), and \( \angle C \) can be determined using the fact that the sum of angles in a triangle is \( 180° \). Thus:
\[
\angle C = 180° - 90° - 25° = 65°
\]
To find the length of \( AC \) using the sine ratio, we can consider the right triangle where:
- \( BC \) (the side opposite angle \( A \)) is the hypotenuse.
- \( AC \) (the side opposite angle \( B \)) is what we want to find.
According to the sine ratio:
\[
\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
For angle \( B \):
\[
\sin(25°) = \frac{AC}{BC}
\]
Since \( BC = 5 \) inches, we can set up the equation:
\[
\sin(25°) = \frac{AC}{5}
\]
From this, we can express \( AC \) as:
\[
AC = 5 \sin(25°)
\]
Thus, the correct choice that uses the sine ratio to find the length of \( AC \) is:
**AC = 5 sin(25°)**.
\[
\angle C = 180° - 90° - 25° = 65°
\]
To find the length of \( AC \) using the sine ratio, we can consider the right triangle where:
- \( BC \) (the side opposite angle \( A \)) is the hypotenuse.
- \( AC \) (the side opposite angle \( B \)) is what we want to find.
According to the sine ratio:
\[
\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
For angle \( B \):
\[
\sin(25°) = \frac{AC}{BC}
\]
Since \( BC = 5 \) inches, we can set up the equation:
\[
\sin(25°) = \frac{AC}{5}
\]
From this, we can express \( AC \) as:
\[
AC = 5 \sin(25°)
\]
Thus, the correct choice that uses the sine ratio to find the length of \( AC \) is:
**AC = 5 sin(25°)**.