To solve the problem you must apply the following proccedure:
1. The information given in the problem is:
- The towers are 1280 meters apart and rise 160 meters above the road.
- The cable between the towers has the shape of a parabola.
- The cable touches the sides of the road midway between the towers.
2. Therefore, you must apply the the standard form of the equation of a parabola with vertex at the origin. The parabola opens up, so:
x^2=4py
3. First, you need to find p:
p=x^2/4y
x=640 when y=160
p=(640)^2/(4x160)
p=640
4. Now you need to find y. The problem asks for the height of the cable 200 meters from a tower, therefore:
x=640-200
x=440
y=x^2/4p
y=(440)^2/(4x640)
y=75.62≈76 m
The answer is: 76 m
