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In triangle ABC, ZA = 25°, ZC = 55°, and AB = 60. What are the approximate measures of the remaining side lengths ofthe triangle?

Sagot :

We have the next given information for the given triangle:

∠A= 25 degrees

∠C = 55 degrees

and

AB=60

To solve this, we need to use the Law of sines, which is given by:

[tex]\frac{\sin(A)}{a}=\frac{\sin(B)}{b}=\frac{\sin(C)}{c}[/tex]

Where ab= b = 60

Solve for a:

[tex]\frac{\sin(A)}{a}=\frac{\sin(B)}{b}[/tex][tex]a=\frac{\sin (A)}{\frac{\sin (B)}{b}}[/tex][tex]a=\frac{b\cdot\sin (A)}{\sin (B)}[/tex]

Replacing the values:

[tex]a=\frac{60\cdot\sin (25)}{\sin (55)}[/tex]

Then:

[tex]a\approx31[/tex]

Now, we need to find the side lenght of c

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