Trigonometry Homework

Question

Consider the three points:

A=(9,2)

B=(3,6)

C=(8,4)

Determine the angle between AB and AC

θa =?

Answer 1

c=AB = sqrt( 36 + 16) = sqrt(52) = 2 * sqrt(13)

b=AC = sqrt( 1 + 4) = sqrt(5)

a=BC = sqrt( 25 + 4) = sqrt(29)

a^2 = b^2 + c^2 - 2bc cos A

29 = 5 + 52 - 2( sqrt(5))(2)(sqrt(13)) cos A

29 = 57 - 4 sqrt(65) cos A

-28 = -4 sqrt(65) cos A

7 = sqrt(65) cos A

7 * sqrt(65) / 65 = cos A

A = 29.7448812969422237349023117187887.......