SOLUTION: Right triangle ABC is graphed on the coordinate plane and has vertices at A(-1, 3), B(0,5), and C(4,3). What is the measure of angle C to the nearest degree?

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Question 723987: Right triangle ABC is graphed on the coordinate plane and has vertices at A(-1, 3), B(0,5), and C(4,3). What is the measure of angle C to the nearest degree?
Answer by josgarithmetic(39614) About Me  (Show Source):
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The angle at point B appears to be the 90 degree angle. You can get the length AC by counting on the graph and get the length AB using Distance Formula. Use Law of Sines.

sin%28B%29%2FAC=sin%28C%29%2FAB
1%2FAC=sin%28C%29%2FAB
sin%28C%29=AB%2FAC
You may be able to use known right-triangle knowledge and avoid Law Of Sines.
AC is 5. AB is sqrt(5)

Solve first for sin(C) and find angle at C. highlight%28sin%28C%29=sqrt%285%29%2F5%29.
Angle at C is about 26.6 degrees.