SOLUTION: From a point 250 m from the base of a vertical cliff, the angles of elevation to the top and bottom of a radio tower on top of the cliff are 62.2 degrees and 59.5 degrees. How tall

Algebra ->  Trigonometry-basics -> SOLUTION: From a point 250 m from the base of a vertical cliff, the angles of elevation to the top and bottom of a radio tower on top of the cliff are 62.2 degrees and 59.5 degrees. How tall      Log On


   

Question 277029: From a point 250 m from the base of a vertical cliff, the angles of elevation to the top and bottom of a radio tower on top of the cliff are 62.2 degrees and 59.5 degrees. How tall is the tower?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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.