Express the Distance d between the plane and the top of the control tower as a function of x?

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1 Answer
May 22, 2018

d=90400ft +x^2.

Explanation:

What we have in this diagram is a large right triangle with two legs 300ft and xft and a hypotenuse root()((300)^2+x^2)ft by the pythagorean theorem,

a^2+b^2=c^2,

and another right triangle standing on top of that hypotenuse. This second, smaller triangle has one leg of 20ft (the height of the building), and another of root()((300)^2+x^2)ft (because this second triangle is standing on the hypotenuse of the other, its length is the length of the hypotenuse of the first) and a hypotenuse of d.

From this, we know that the hypotenuse of the smaller triangle, once again making use of the pythagorean theorem, is equal to

d=(20)^2ft + (root()((300)^2+x^2))^2ft
d= 400ft + (300)^2ft+x^2ft
d=400ft + 90000ft+x^2ft
d=90400ft +x^2ft.