SOLUTION: Would I be able to get help on this question? (( If A is (2,3) and B (3,7) find the angle between AB and the x-axis ))

Algebra ->  Equations -> SOLUTION: Would I be able to get help on this question? (( If A is (2,3) and B (3,7) find the angle between AB and the x-axis ))       Log On


   

Question 976346: Would I be able to get help on this question? (( If A is (2,3) and B (3,7) find the angle between AB and the x-axis ))
Found 2 solutions by Fombitz, Alan3354:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
AB=(3-2,7-3)=(1,4)
You can use the dot product or trigonometry.
.
.
.

Dot product with unit x vector (1,0).
(1,4)*(1,0)=1*1+4*0=1
A%2AB=abs%28A%29%2Aabs%28B%29%2Acos%28theta%29
abs%28A%29=sqrt%281%5E2%2B4%5E2%29=sqrt%281%2B16%29=sqrt%2817%29
abs%28B%29=1
1=sqrt%2817%29%2A1%2Acos%28theta%29
cos%28theta%29=1%2Fsqrt%2817%29
theta=75.96
.
.
.
Using trigonometry,
sin%28theta%29=y%2Fsqrt%28x%5E2%2By%5E2%29
sin%28theta%29=4%2Fsqrt%281%5E2%2B4%5E2%29
sin%28theta%29=4%2Fsqrt%2817%29
theta=75.96

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
If A is (2,3) and B (3,7) find the angle between AB and the x-axis
----------
Translate A & B so that A is at the Origin.
A' = (0,0)
B' = (1,4)
tangent = y/x = 4
Angle = 75.96 degs
======================
Or,
Slope m = diffy/diffx
m = (7-3)/(3-2) = 4/1
m = 4 = tangent of the angle
etc