Daniel O. answered • 10/22/12

Math and Physics Tutor, with a math and physics degree

This is where drawing a diagram can be very helpful, as it makes things much easier to explain and understand.

I'm assuming the 90 degree angle must be the one made by the x-axis and y-axis, so we need to find the lengths of the sides of the triangle that are on the x and y axes. The lengths will be given by the x and y intercepts. First we'll find the x-intercept, by letting y = 0, then adding 2 to both sides, then dividing both sides by 4:

0 = 4x - 2 =====> 2 = 4x =====> x = 2/4 = 1/2. So the x-intercept is x = 1/2. Now we let x = 0 to find the y-intercept:

y = 4(0) - 2 ====> y = -2, so that is the y-intercept.

Now we have a triangle with one side having a length 2, and the other side length 1/2 (the third side is the hypotenuse created by y = 4x - 2). Since it's a right-triangle, from here we can use tanθ = 2/(1/2), so tanθ = 4, so use tan^{-1}4 thus θ = 75.96 degrees. Since the three angles must add to 180 degrees, the other angle must be 14.04 degrees.