How tall is the golden gate bridge from the road

Asked by admin @ 29/10/2021 in Mathematics viewed by 251 People

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.

Answered by admin @ 29/10/2021

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

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