All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 A tall tower (Posted on 2014-06-18)
A tall tower is constructed on the side of a hill with uniform incline. Two guy wires are attached to the top of the tower and to points on the ground 50.0 feet from the tower - one directly up-slope and one directly down-slope. If the wires are 284.7 feet and 303.5 feet respectively, what is the angle of incline of the hill and how high is the tower?

 No Solution Yet Submitted by Jer No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 Solution - Spoiler | Comment 2 of 6 |
If the slope is angle A to the horizontal, then the angle of the tower to the slope is 90-A on the uphill side and 90+A on the downhill side. (Tower is assumed vertical). Tower height is "h".

Consider the two triangles formed by the tower, wires and slope.  Using the law of cosines:
Uphill side: 284.7^2=h^2+50^+2*h*50*cos(90-A)
Note; cos(90-A)=sin(A)
Downhill side: 303.5^2=h^2+50^+2*h*50*cos(90+A) Note: cos(90+A)=-sin (A)

Adding the two equations eliminates A, and therefore h=288.97.

Plugging this value back into one of the cosine equations gives A = 10.99 deg

REF: Bractals' question - it does seem like the answer was intended to give integer results

 Posted by Kenny M on 2014-06-18 20:48:18

 Search: Search body:
Forums (0)