SOLUTION: Let A = (0, 0), B = (1, 2), C = (6, 2), D = (2, −1), and E = (1, −3). Show that angle CAB is the same size as angle EAD

Algebra ->  Angles -> SOLUTION: Let A = (0, 0), B = (1, 2), C = (6, 2), D = (2, −1), and E = (1, −3). Show that angle CAB is the same size as angle EAD       Log On


   

Question 1078300: Let A = (0, 0), B = (1, 2), C = (6, 2), D = (2, −1), and E = (1, −3). Show that angle
CAB is the same size as angle EAD
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Find slopes of CA and BA
+m%5B1%5D+=+%28+2+-+0+%29+%2F+%28+6+-+0+%29+
+m%5B1%5D+=+1%2F3+
----------------
+m%5B2%5D+=+%28+2+-+0+%29+%2F+%28+1+-+0+%29+
+m%5B2%5D+=+2+
----------------
Find the angles that CA and BA make
with the horizontal
+arctan%28+1%2F3%29+=+18.4349+ degrees
+arctan%28+2+%29+=+63.4349+
Find the angle between CA and BA
+63.4349+-+18.4349+=+45+ degrees
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Find slopes of EA and DA
+m%5B3%5D+=+%28+-3+-+0+%29+%2F+%28+1+-+0+%29+
+m%5B3%5D+=+-3+
------------------
+m%5B4%5D+=+%28+-1+-+0+%29+%2F+%28+2+-+0+%29+
+m%5B4%5D+=+-1%2F2+
------------------
Find angles that EA and DA make with
the horizontal
+arctan%28+-3+%29+=+-71.5651+
+arctan%28+-1%2F2+%29+=+-26.5651+
Find the angle between EA and DA
+-26.5651+-%28+-71.5651+%29+=+45+ degrees
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CAB and EAD are both 45 degrees