3 years ago

Please Please help!

Mathematics

1 answer:

sergiy2304 [10]3 years ago

8 0

They are vertical angles and congruent angles.

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Let's assume they meant C=40 degrees. With an angle like that they're asking for approximation; we'll oblige.

The circumradius is the product of the triangle sides divided by four times the area.

Here we have remaining side given by the Law of Cosines.

$AB^2 = AC^2 + BC^2 - 2\ AC \ BC \cos C$

$AB^2 = AC^2 + BC^2 - 2 AC \ AB \cos C = 5^2 + 12^2 - 2(5)(12) \cos 40^\circ$

$AB = \sqrt{ 169 - 120 \cos 40 ^\circ} \approx 8.77921789$

The area is $\frac 1 2\ AC \ BC \sin C = \frac 1 2 (5)(12) \sin 40^\circ \approx 19.283628$

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