Perpendicular and parallel

Find the value of t if 2tx+5y-6=0 and 5x-4y+8=0 are perpendicular and parallel lines. What angle does each line make with the x-axis, and find the angle between the lines?

Correct answer:

t1 =  2
A1 =  -38.6598 °
A2 =  -128.6598 °
t2 =  -3.125
B1 =  51.3402 °
B2 =  -128.6598 °

Step-by-step explanation:

2tx+5y6=0 5x4y+8=0  n1 = (2t; 5) n2 = (5; 4)  normal n1.n2 = 0  2 t1 5+5 (4)=0  10t1=20  t1=1020=2  t1=2
A1=π180°arctan2 t1590=π180°arctan2 2590=38.6598=38°3935"
A2=π180°arctan5490=128.6598=128°3935"
parallel n1 = k   n2 k=5/(4)=45=141=1.25  2 t2=5/(4) 5  2t2=6.25  t2=26.25=3.125  t2=825=3.125
B1=π180°arctan2 t2590=π180°arctan2 (3.125)590=51.3402=51°2025"
B2=π180°arctan5490=128.6598=128°3935"



Did you find an error or inaccuracy? Feel free to write us. Thank you!







Tips for related online calculators
The line slope calculator is helpful for basic calculations in analytic geometry. The coordinates of two points in the plane calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of the segment, intersections of the coordinate axes, etc.
Our vector sum calculator can add two vectors given by their magnitudes and by included angle.
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
See also our trigonometric triangle calculator.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.

You need to know the following knowledge to solve this word math problem:


 
We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions: