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Posted by **Cathy** on Thursday, October 11, 2012 at 4:24am.

- trigonometry -
**Damon**, Thursday, October 11, 2012 at 5:27amangle a is from tan a = 105/x

angle b = 3.33333 so tan b = 0.05824

tan (a+b) = 130/x

tan (a+b) = (tan a + tan b)/(1 - tan a tan b)

130/x = (105/x + .05824) / (1-6.115/x)

130/x = (105 + .05824 x) / (x - 6.115)

130 (x-6.115) = 105 x + .05824 x^2

130 x - 795 = 105 x + .0524 x^2

.0524 x^2 - 25 x + 795 = 0

x^2 - 477 x + 15172 = 0

x = [ 477 +/- sqrt (227529 -60688)]/2

x = [ 477 +/- 408 ] / 2

x = 442 or 34.5

- trigonometry -
**Reiny**, Thursday, October 11, 2012 at 8:30amUnless I am totally mis-reading the question .....

height of tower + flag pole = 130

distance from base of tower ---- x

tan 3°20' = 130/x

x = 130/tan3°20' = appr 2232 ft

- trigonometry -
**Steve**, Thursday, October 11, 2012 at 11:10amWhen you get an answer, be sure to do a sanity check. Considering what a small angle 3°20' is, you'd expect the distance to be very large. Even 442 would make for an angle much greater than 3°20'.

Without even doing the math, Reiny's answer makes much more sense that Damon's. Sorry, Man. :-(

Just a comment.

- trigonometry -
**Damon**, Thursday, October 11, 2012 at 2:13pmAh, it did not ask for the angle between the base of the building and the top of the pole. It asked for the tiny angle subtended by the 25 foot pole alone.

To get a rough approximation do

fan 3.33 = 25/x

x = 430 ft

- trigonometry -
**Steve**, Thursday, October 11, 2012 at 3:03pmDang - you are correct, Damon. Sorry, Reiny.

- trigonometry -
**Cathy**, Friday, October 12, 2012 at 4:41amThanks all of you for the help...

Damon's process is correct. However, he just failed to write the equations properly for the last 6 lines.

"0.0524" should be "0.05824".

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