Answer:
A) a = 11.08 and b = 12.94
Step-by-step explanation:
We will use the law of sines to answer this problem.
First we find the measure of the missing angle. The sum of the measures of the angles of a triangle is 180°. The two given angles are 58 and 82; this gives us 58+82 = 140°. This leaves the third angle as 180-140 = 40°.
The law of sines is
[tex]\frac{\sin{A}}{a}=\frac{\sin{B}}{b}=\frac{\sin{C}}{c}[/tex]
We have the measures of ∠C and side c; this makes the first ratio in our proportion
[tex]\frac{\sin{40}}{8.4}[/tex]
To find the measure of side a, our proportion will be
[tex]\frac{\sin{40}}{8.4}=\frac{\sin{58}}{a}[/tex]
Cross multiplying, we have
a(sin 40) = 8.4(sin 58)
Divide both sides by (sin 40):
a(sin 40)/(sin 40) = 8.4(sin 58)/(sin 40)
a = 11.08
To find the length of side b, we use our original ratio
[tex]\frac{\sin{40}}{8.4}[/tex]
and the proportion
[tex]\frac{\sin{40}}{8.4}=\frac{\sin{82}}{b}[/tex]
Cross multiplying,
b(sin 40) = 8.4(sin 82)
Divide both sides by (sin 40):
b(sin 40)/(sin 40) = 8.4(sin 82)/(sin 40)
b = 12.94
