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

a flagpole 25 feet high stands on the top of a tower, which is 105 feet high. at what distance from the base of the tower will the flagpole subtend an angle of 3 degrees, 20 minutes?

- trigonometry -
**Damon**, Thursday, October 11, 2012 at 5:27am
angle 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 8:30am
Unless 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 11:10am
When 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 2:13pm
Ah, 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 3:03pm
Dang - you are correct, Damon. Sorry, Reiny.

- trigonometry -
**Cathy**, Friday, October 12, 2012 at 4:41am
Thanks 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".

## Answer This Question

## Related Questions

- math - if Amy stands 36 feet from a flagpole and the angle formed from the top ...
- math - A radio tower stands on the top of a hill that is 85 feet high. From the ...
- Trigonometry - a flagpole 25 feet tall stands on a top of a building. from a ...
- Trigonometry - a flagpole 25 feet tall stands on a top of a building. from a ...
- Math - A man standing 20 m from a tower estimates the angle of elavation of the ...
- TRIG Help help help test tommarow - A TV tower stands on top of the Empire State...
- MATH - A wire is stretched from the ground to the top of an antenna tower. The ...
- trig - On an inclined road, which makes an angle of 25 degrees with the ...
- math models - The Sears Tower in Chicago is 1454 feet high. Sketch and find the ...
- Pre-Calculus - A wire from the top of a TV tower makes an angle of 49.5 with the...

More Related Questions