Problem $4(200$ Points$)$:

The vertical angle to the top of the flagpole from point $A$ on the ground is observed to be $60.$ The observer walks $10$ ft directly away from the flagpole from point A to point B and finds the new angle to be $45.$ What is the approximate height of the flagpole. $($Show your calculation process$)$

$(tan60-tan45)x=10**tan60**tan45$

$x=\frac{10**tan60}{tan60-tan45}=23\mathrm{.}66ft$