Question 148656: find all the angles in a 5-12-13 triangle.
Answer by nabla(475)   (Show Source):
You can put this solution on YOUR website! We first note that
5^2+12^2=13^2
25+144=169
169=169.
So, this is a right triangle by the Pythagorean Theorem. It follows that one angle is 90 degrees.
So, we need only find the measures of angles opposite 5 and 12. Let's call them a and b. Note that a+b=90.
Cos(a)=adj/hyp=12/13
Cos(b)=adj/hyp=5/13
So we want to take ArcCos of 12/13 and 5/13 to find the measures of the remaining angles.
ArcCos(12/13)=.3948 radians
ArcCos(5/13)=1.1760 radians
Multiply radians by 180/pi to get degrees.
So we have 90, 22.62, 67.38 measures in degrees for angles.
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