One tower is 50 ft high and another tower is 30 ft high. The towers are 150 ft apart.?

Question

One tower is 50 ft high and another tower is 30 ft high. The towers are 150 ft apart. A guy
wire is to run from a point A located on the ground between the two towers to the top of
each of the towers.
a) Locate Point A so that the total length of guy wire is minimized.
b) Show in general that regardless of the height of the towers, the length of guy wire is
minimized if the angles at A between the wire and the ground are equal.

I think I have part a) but mainly need help with b). Any feedback would be amazing :)

Answer 1

Draw a diagram. Let x = the distance from point A to the base of the 50' tower. Then 150-x is the distance from point A to the base of the 30' tower. There are two right triangles that form. The first formed by the 50' tower has hypontenuse (which is the distance from the top of the tower to point A) of length = sqrt (50^2 + x^2). The second formed by the 30' tower has hypotenuse (which is the distance from the top of the tower to point A) of length = sqrt (30^2 + (150 - x)^2). You want to minimize the length of the two hypotenuses (hypoteni?). If you graph the following function (it's not pretty!)

y = sqrt (2500 + x^2) + sqrt (900 + 22500 - 300 x + x ^2)

and find the minimum you will have your first answer. The min of this graph is at approx x = 93.9, y = 170.

Answer 2

it form of feels to me that you've arrived at an emotional answer on your question even till now you requested it right here. that's meant to be an purpose clinical communication, yet once you've already predisposed to trust what you favor to trust, then your question isn't some thing better than political rhetoric. i think the mission you worry about is in Loudonville, lengthy island. there has been a number of unproven hypothesis that cell phones would have unknown well being consequences. the precedence, notwithstanding, isn't for the overall ambient, for for the fellow person of the cellular telephone who's protecting the phone hostile to the ear - inches faraway from the mind. notwithstanding, there is not any incredibly evidence of any link between cellular telephone utilization and damaging well being consequences. You look declaring that till that's shown that there is not any damage, then cellular telephone towers might want to no longer be equipped close to colleges. How close to? the college in Loudonville is extremely about 1500 ft from the proposed tower region. Is that too close? What about skill damage to babies who're basically using down Rt. 9? If that's a issue, then the logical extension of your argument is that there will be no cellular telephone towers everywhere till there is evidence that they reason no damage. If cellular telephone transmissions have damaging well being consequences, then radio and television transmissions have a similar consequences. And storage door openers, and residential instant networks, and the keyless get authentic of entry to device on your motor vehicle, and the device that enables you to initiate you motor vehicle contained in the iciness from interior your position, and the interior of reach community that enables the sales clerk on the Apple shop to ring up your sale even as status contained in the technique the tutor room, and the distant administration you take advantage of to exhibit your vacation lighting fixtures on and stale, and so on, and so on, and so on. regrettably, there is nowhere contained in the international you could bypass to dodge those technologies.

Answer 3

Your answer to a) should have come from a parabolic equation whose minimum is the point you chose.

Answer 4

I believe that its two triangles you are looking for. they need to be similar so all the angles in the triangles are the same.