Three vertices of △ABC have coordinates: A(1, 1), B(4, 1), and C(4, 5). What are the cosines of the angles of the triangle?

Question

Three vertices of △ABC have coordinates: A(1, 1), B(4, 1), and C(4, 5). What are the cosines of the angles of the triangle?

cos ∠ABC =?

cos ∠BAC = ?

cos ∠ACB =?

Answer 1

Plot the points, it's a right triangle with angle ABC =90, cosABC = 0

ACB = CAB = 45 degrees

cosACB = cosCAB = cos45 = sqr2/2 = 1.414/2 = 0.707