Acellus
Find all the missing elements:
B
C
a
B = 32°
C = 125°
a = 7
Α'
b C
A = [?]° b = [ ] c = [ ]
Enter

Answer:

A = 23°

B = 9.5

C = 14.7

Step-by-step explanation:

Right Answers :)

The missing values are:

A = 23°

b = 9.5

c = 14.72

"It is a triangle whose one of the angles measure greater than 90° and other two acute angles."

"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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