Question

The relative positions of an aircraft runway and an a = 20-foot-tall control tower are shown in the figure. The beginning of the runway is at a perpendicular distance of 300 feet from the base of the tower. If x denotes the distance an airplane has moved down the runway, express the distance d between the airplane and the top of the control tower in terms of x.

Answer 1

can you find the distance from the airplane to the bottom of the tower ?
It looks like you can use pythagoras to find this distance. Can you ?

Answer 2

i tried but i dont know what to plug in for d

Answer 3

http://staff.tuhsd.k12.az.us/msinkovic/Analysis/2.1%20homework.pdf

here is a link to a picture of the problem it is number 69

Answer 4

First, can you write down the pythagorean theorem for the triangle ?
c is the distance to the bottom of the tower (not the top, but we will get to that in a minute)

Answer 5

Do you know pythagoras ?
http://www.regentsprep.org/Regents/math/geometry/GP13/Pythag.htm

Answer 6

yeah

Answer 7

the answer is d(x) = Square root of: 90,400 + x^2

Answer 8

i dont know how to get there thought (aka why im asking)

Answer 9

ok, but the first step is, can you write down pythagoras for the triangle formed by the bottom of the tower (not the top), as drawn up above?
c^2 = ?

Answer 10

you mean: 900+X^2 ?

Answer 11

right idea, but 300^2 is not 900

Answer 12

oh yeah omg careles error

Answer 13

so c^2 = 300^2 + x^2

Answer 14

now draw a triangle from the plane to the base of the tower, then up 20

Answer 15

ok

Answer 16

the distance along the bottom is c
the distance up is 20
the hypotenuse is d

can you write down pythagoras for this triangle ?

Answer 17

but c^2 = 90000+x^2

Answer 18

so d^2 = 400 + c^2

replace c^2 with 90000 + x^2
d^2 = 400 + 90000 + x^2

can you finish ?

Answer 19

yeah thanks so much!