Light between 2 towers reflecting off a lake

[ArmChairPhysicist]

To this?

 

[ArmChairPhysicist]

Cancel out the denominator, then square both sides?

 

[ArmChairPhysicist]

Which gets me this.

 

[Ray Vickson]

View attachment 196047 To this?

Well, the answer is yes, since you have done exactly what I suggested. However: please do not continually ask questions as to whether your next step is correct or not---just work it all out, from beginning to the end (or, at least, as FAR as you can). Try to develop some confidence in your own work.

 

[ArmChairPhysicist]

Now I simply solve for x?

 

[ArmChairPhysicist]

Ok thank you

 

[ArmChairPhysicist]

Thank you so much for your help and time.

 

[Dick]

The 141 came from me taking the derivative of 21^2+(120-x)2

2 • 21 ^2-1 =
42

(120-x)^2 = 2(120-X)^1 correct?

Not correct. The derivative of $21^2$ is zero. It's a constant.