lines a(1) and a(2 in two-dimensional space intersect at a point, forming an acute angle A. the slope of a(1) is square root of 5 , and cos A= 2/9. What is the slope of a(2)? There are two answers, both must be given to properly answer the question
tanθ1 = √5, tanA = √(77)/2 (since cosA = 2/9, and A is an acute angle.)
tanθ2 = m, where m is the slope to be found.
Since θ2-θ1 = ±A,
m = tan(θ1±A) = [tanθ1±tanA]/[1-+tanθ1*tanA]
Plugging in tanθ1 = √5, tanA = √(77)/2 gives you the exact final answers.
Answer in decimal form: m = -.199 or m = -.752.