Answer:
A) [tex]\frac{\sin{23}}{6.2}=\frac{\sin{85}}{b}[/tex]
Step-by-step explanation:
In order to use the Law of Sines, we must have a known angle and the known side opposite it.
The only side measure we have is that of AB, which is 6.2. The angle opposite this is ∠C, which we do not have the measurement of.
We do have the measurement of ∠A and ∠B; we can use these to find the measure of ∠C. We know that the sum of the measures of the angles in a triangle is 180°; this means
m∠C = 180-(72+85) = 180-157 = 23°
This makes the first ratio in the Law of Sines
[tex]\frac{\sin{23}}{6.2}[/tex]
We are trying to find the measure of b. This means we use the angle opposite b, ∠B; m∠B = 85°. This gives us the ratio
[tex]\frac{\sin{85}}{b}[/tex]
Together, this gives us the proportion
[tex]\frac{\sin{23}}{6.2}=\frac{\sin{85}}{b}[/tex]
