find a formula for theta , the angle formed by the intersection of L1 & L2 let L1 and L2 be non parallel lines of slope m1 and m2. m1>m2>0
To find the formula for the angle θ formed by the intersection of two non-parallel lines L1 and L2 with slopes m1 and m2, where m1 > m2 > 0, we can use the properties of slopes and trigonometry.
First, we know that the slopes of two lines can be related to the tangent of the angle between them. The tangent of an angle is equal to the ratio of the difference in y-coordinates to the difference in x-coordinates for any two points on the lines. Mathematically, we represent this relationship as:
tan(θ) = | (m2 - m1) / (1 + m1 * m2) |
Now, to find the formula for θ, we need to solve for it. Since m1 > m2 > 0, we know that the denominator (1 + m1 * m2) will always be positive. Therefore, we can simplify the equation to:
θ = arctan(|(m2 - m1) / (1 + m1 * m2)|)
This formula gives us the angle θ in radians. If you want the answer in degrees, you can convert it by multiplying the result by (180/π).