Hello, rcmango!

Edit: Captain Black's is brilliant!

I totally forgot about that "reflection trick' . . . (*kick self*)

You are trying to photograph a bird sitting on a tree branch,

but a tall hedge is blocking your view.

However, as the drawing shows, a plane mirror reflects light from the bird into your camera.

If x = 3.0 m and y = 4.2 m, for what distance must you set the focus of the camera lens

in order to snap a sharp picture of the bird's image? We can solve this without trig . . . Code:

E 2.1 D
+ - * - - - *
. . . : * |
. . . : * | a
. . . : * |
. . . : * C
. 4.2 : * |
. . . : * |
. . . : * | 4.2-a
. . . : * |
. . . : * |
. . . * - - - - - *
. . . A 3.0 B

Note that: .$\displaystyle \Delta CDE \sim \Delta CBA$

. . Hence: .$\displaystyle \frac{a}{2.1} \:=\:\frac{4.2-a}{3}\quad\Rightarrow\quad a\:=\:\frac{147}{85}\;\;{\color{blue}[1]}$

The distance is: .$\displaystyle AC + CE \;=\;\sqrt{(4.2-a)^2 + 3^2}+ \sqrt{a^2+ 2.1^2}\;\;{\color{blue}][2]} $

I'll let *you* substitute [1] into [2] . . .