Question

Two different boats leave from point A(1, 2) in direction of points B(3, 8) and C(7, 4) in order to look for Pooja. Determine the angle between the directions of the two boats. (Hint: Determine the angle between sides AB and AC)

Answer 1

53.13°

Explanation:

angle between AB & x-axis (α):

`tan\ \alpha=(yB-yA)/(xB-xA)`

`=(8-2)/(3-1)`

= 3

α = 71.57°

angle between AC & x-axis (β):

`tan\ \beta=(yC-yA)/(xC-xA)`

`=(4-2)/(7-1)`

`(1)/(3)`

β = 18.43°

angle between AB & AC:

α - β = 71.57° - 18.43°

= 53.13°