The towers of the golden gate bridge connecting san francisco to marin county are 1280 meters apart and rise 160 meters above the road. the cable between the towers has the shape of a parabola and the cable just touches the sides of the road midway between the towers. what is the height of the cable 200 meters from a tower? round to the nearest meter.

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 t he 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