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January 26, 2015

January 26, 2015

Posted by **rhen songalia** on Tuesday, July 16, 2013 at 9:18am.

- plane and trigonometry -
**Steve**, Tuesday, July 16, 2013 at 10:13amYou have only given one angle, but I'll call the unknown angle A and assume it is the angle to the top of the pole.

Your mission, should you choose to accept it, is to fill in the missing data and follow the logic to a final solution.

If the observer is x feet from the base of the tower (that is x+20 feet from the center of the base of the tower),

and if the height of the tower is h,

h/x = tan 30 = 1/√3

(h+30)/(x+20) = tan A

equating the two expressions for x, we get

√3 h = (h+30)/tanA - 20

h = (30 cotA - 20)/(√3 - cotA)

If A is the angle of the tower, not the pole, then you got some fixing to do.

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