Question 277029
let x be the larger angle = 62.2 degrees


let y be the smaller angle = 59.5 degrees.


let a be the vertical distance from the base of the vertical cliff to the top of the tower.


let b be the vertical distance from the base of the vertical cliff to the bottom of the tower.


the height of the tower would be a minus b.


tan(x) = opposite/adjacent = a/250


tan(y) = opposite/adjacent = b/250


this means that a = 250*tan(x).


this also means that b = 250*tan(y).


this also means that a - b = 250*tan(x) - 250*tan(y) which means that:


a-b = 250*(tan(x)-tan(y).


finally, this means that:


a-b = 250 * (tan(62.2) - tan(59.5)).


we use our calculator to find the tangents and plug into the formula to get


a-b = 250 * (1.896668769 - 1.697663119) which becomes:


a-b = 250 * .19900565 which becomes:


a-b = 49.75141253 meters.