Asked by ako
                the vertices of the triangle one at (7,4) (1,7) and (-3,-4). find the interior L at the vertex (7,4).
            
            
        Answers
                    Answered by
            oobleck
            
    It appears that "interior L" means the interior angle at (7,4)
So, call the three vertices A,B,C and you want angle A.
the slope of AB is -1/2
The slope of AC is 4/5
That makes the angles that AB and AC make with the +x-axis
AB: -26.56°
AC: 38.66°
Thus the angle between AB and AC is 26.56+38.66 = 65.22°
or, we can get the lengths of the sides:
AB = √(3^2+6^2) = √45
AC = √(8^2+10^2) = √164
BC = √(11^2+4^2) = √137
Now the law of cosines says that
a^2 = b^2+c^2 - 2bc cosA
137 = 164 + 45 - 2√7380 cosA
cosA = 6/√205
A = 65.22°
    
So, call the three vertices A,B,C and you want angle A.
the slope of AB is -1/2
The slope of AC is 4/5
That makes the angles that AB and AC make with the +x-axis
AB: -26.56°
AC: 38.66°
Thus the angle between AB and AC is 26.56+38.66 = 65.22°
or, we can get the lengths of the sides:
AB = √(3^2+6^2) = √45
AC = √(8^2+10^2) = √164
BC = √(11^2+4^2) = √137
Now the law of cosines says that
a^2 = b^2+c^2 - 2bc cosA
137 = 164 + 45 - 2√7380 cosA
cosA = 6/√205
A = 65.22°
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