Question

In the triangle shown, m∠C=38° 𝑚 ∠ 𝐶 = 38 ° and c = 22 mi. Which equation shows how the Law of Sines can be used to find a? (1 point) Responses sin38°22 mi.=sin90°a sin ⁡ 38 ° 22 mi. = sin ⁡ 90 ° 𝑎 the fraction with numerator sine 38 degrees and denominator 22 mi. is equal to the fraction with numerator sine 90 degrees and denominator A sin52°22 mi.=sin38°a sin ⁡ 52 ° 22 mi. = sin ⁡ 38 ° 𝑎 the fraction with numerator sine 52 degrees and denominator 22 mi. is equal to the fraction with numerator sine 38 degrees and denominator A sin90°22 mi.=sin52°a sin ⁡ 90 ° 22 mi. = sin ⁡ 52 ° 𝑎 the fraction with numerator sine 90 degrees and denominator 22 mi. is equal to the fraction with numerator sine 52 degrees and denominator A sin38°22 mi.=sin52°a sin ⁡ 38 ° 22 mi. = sin ⁡ 52 ° 𝑎

c i s the top angle b is the right angle and a is the bottom angle. ca is the hypotenuse and is b ab is c and cb is a

Answer 1

To use the Law of Sines in the triangle you described, we first need to identify the angles and sides. Since it is stated that \( m∠C = 38° \) and \( c = 22 \text{ mi} \) (where \( c \) is the side opposite angle \( C \)), and angle \( B \) is given as a right angle (90°), we can infer that angle \( A \) can be found using the triangle angle sum property.

Given:
- \( m∠B = 90° \)
- \( m∠C = 38° \)
- Thus, \( m∠A = 180° - m∠B - m∠C = 180° - 90° - 38° = 52° \)

Now we have:
- Angle \( A = 52° \)
- Angle \( B = 90° \)
- Angle \( C = 38° \)
- Side \( c = 22 \) mi (opposite angle \( C \))

According to the Law of Sines:
\[
\frac{a}{\sin A} = \frac{c}{\sin C}
\]
Substituting the values we have:
\[
\frac{a}{\sin 52°} = \frac{22 \text{ mi}}{\sin 38°}
\]

This translates to the equation:
\[
\sin 52° \cdot 22 \text{ mi} = \sin 38° \cdot a
\]

Therefore, the correct choice to represent how the Law of Sines can be used to find \( a \) is:
\[
\sin 38° \cdot 22 \text{ mi} = \sin 52° \cdot a
\]

So the best answer among the provided options would be:
\[
\sin 38° / 22 \text{ mi.} = \sin 52° / a
\]

In summary, the answer that shows how the Law of Sines can be used to find \( a \) is:
\[
\sin 52° / 22 \text{ mi.} = \sin 38° / a
\]