Finding the acute angle between the following pairs of lines.

Question

I don't understand how to find an acute angle between 3y= x - 7 and 2y= 3 - 4x. 

Could you help me? 

Answer 1

 

 

 

Find the slope (m)of each line.

3y= x - 7

 

y=(1/3)x -7/3

 

slope (m)=1/3

 

 

2y= 3 - 4x

 

y=(-4/2 )x + 3

 

y=-2x+3

 

slope (m)=-2

 

Find the angle of inclination of each line, using θ=tan⁻¹m

 

θ=tan^-1 (1/3)=18.43

 

θ= tan^-1 (-2)=-63.43=63.43

Subtract the two angles.

 

63.43-18.43=45

 

So acute angle is 45 degress

 

Handle the case where this difference is not an acute angle. (If you get a negative angle, take its absolute value. Also, when two lines intersect, they form two pairs of equal angles. Unless the lines are perpendicular, one pair will be acute and the other obtuse. You want to find the acute pair, so if you calculated the obtuse pair just subtract the value from pi radians or 180° to get the acute values.)