Question 302049: a cellular phone tower services a 20 mile radius. A rest stop on the highway is 5 miles east and 12 miles north of the tower. If you continue driving due east, for how many miles will you be in range of the tower?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! a cellular phone tower services a 20 mile radius.
A rest stop on the highway is 5 miles east and 12 miles north of the tower.
If you continue driving due east, for how many miles will you be in range of the tower?
:
Let x = no. of miles east of the rest stop to max range (20 mi from center)
:
Draw a diagram.
A circle, draw inside a rectangle 12n by 5w, lower left corner is at the center.
The upper right corner is the rest stop, label the line from rest stop to a
point on the circumference as x, from this same point a radius line to the center.
This is a right triangle we can solve; a^2 + b^2 = c^2
a = 12
b = (x+5)
c = 20
:
12^2 + (x+5)^2 = 20^2
144 + x^2 + 10x + 25 = 400
x^2 + 10x + 144 + 25 - 400 = 0
A quadratic equation
x^2 + 10x - 231 = 0
Factors to
(x-11)(x+21) = 0
x = 11 mi east from rest stop to max range point
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