SOLUTION: Please help me with this word problem: A guy wire of length 50 feet is attached to the ground and to the top of an antenna. The height of the antenna is 10 feet larger than the di

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Please help me with this word problem: A guy wire of length 50 feet is attached to the ground and to the top of an antenna. The height of the antenna is 10 feet larger than the di      Log On


   

Question 87089: Please help me with this word problem:
A guy wire of length 50 feet is attached to the ground and to the top of an antenna. The height of the antenna is 10 feet larger than the distance from the base of the antenna to the point where the guy wire is attached to the ground. What is the height of the antenna?
Answer by Flake(45) About Me  (Show Source):
You can put this solution on YOUR website!
---Step#1: Draw the problem out to visualize.
You should draw a right-triangle.
The slant of the triangle is the guy-wire = 50ft.
The base of the antenna to the guy-wire on the ground is say "x"
The height of the antenna is 10 feet larger than the distance from the base of the antenna to the point where the guy wire is attached to the ground = (x+10)
---Step#2: Solving
Rewrite a%5E2+%2B+b%5E2+=+c%5E2+; where
a = x
b = (a+10)
c = 50
becomes x%5E2+%2B+%28x%2B10%29%5E2+=+50%5E2+
becomes x%5E2+%2B+x%5E2%2B20x%2B100+=+2500+
becomes 2x%5E2%2B20x-2400+=+0+
becomes x%5E2%2B10x-1200+=+0+
solve with x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
Once you have x, length of antenna is x+10