The missing values are:
A = 23°
b = 9.5
c = 14.72
What is obtuse triangle?
"It is a triangle whose one of the angles measure greater than 90° and other two acute angles."
What is law of sines?
"The ratio of the length of a side of a triangle to the sine of the angle opposite to that side is the same for all sides and angles in a given triangle."
For given question,
We have been given an obtuse triangle ABC.
Here, ∠B = 32°
∠C = 125°
We know that the sum of all angles of a triangle is 180°
⇒ ∠A + ∠B + ∠C = 180°
⇒ ∠A + 32° + 125° =180°
⇒ ∠A = 23°
Using the law of sines to triangle ABC,
[tex]\Rightarrow \frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC} \\\\\Rightarrow \frac{7}{sin23^{\circ}} =\frac{b}{sin32^{\circ}} =\frac{c}{sin125^{\circ}}[/tex]
Consider,
[tex]\Rightarrow \frac{7}{sin23^{\circ}} =\frac{b}{sin32^{\circ}} \\\\\Rightarrow \frac{7}{0.39} =\frac{b}{0.53} \\\\\Rightarrow 7\times 0.53=b\times 0.39\\\\\Rightarrow b = 9.5[/tex]
Now we find the length of the side AB.
[tex]\Rightarrow \frac{7}{sin23^{\circ}} =\frac{c}{sin125^{\circ}} \\\\\Rightarrow \frac{7}{0.39} =\frac{c}{0.82} \\\\\Rightarrow 7\times 0.82=c\times 0.39\\\\\Rightarrow c = 14.72[/tex]
Therefore, the missing values are:
A = 23°
b = 9.5
c = 14.72
Learn more about the law of sines here:
https://brainly.com/question/17289163
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