We can add ax to both sides of the equation to get all the x's on the same side.
Our Equation: bx = ad -ax
After Addition: bx + ax = ad
Now we can factor the x out on the left side of the equation.
Our Equation: bx + ax = ad
After Factoring: x (b+a) = ad
Then we can solve for x by dividing both sides by (b+a).
Our Equation: x (b+a) = ad
After Division: x = ad/ (b+a)
Now we can plug in our solution for x into the equation we would use to find the tangent of θ. Tangent equals opposite/hypotenuse.
Equation For Finding The Tangent Of θ: tanθ = x/a
After Plugging in solution: tanθ = ad/ (a+b) * 1/a
We can simplify the equation by dividing the a's out of the equation.
Our Equation: tanθ = ad/ (a+b) * 1/a
Now Simplified: tanθ = d/ (a+b)
So now we can simplify it even further by taking the tan out of both sides.
Our Equation: tanθ = d/ (a+b)
Becomes: θ = tan-1 (d/a+b))
This is how we can find the angle we need to make accurate bank shots. To see an example, click next. You can click back to go back, or home to go back to the homepage.
