Question

A particular type of bridge can fold up to allow boats to pass by. Each folding part of the bridge is 64 m long and makes

a 70° angle to the horizontal when fully raised. How far apart are the ends of the raised parts when the bridge is fully

opened?

Answer 1

The distance between the ends of the raised parts when the bridge is fully opened is approximately 60.771 meters.

Step-by-step explanation:

To find the distance between the ends of the raised parts when the bridge is fully opened, we need to use trigonometry. When the bridge is fully raised, it forms a right-angled triangle with one side being the length of the folding part (64 m) and the other side being the horizontal distance between the ends of the folding parts. We can use the sine function to solve for this distance:

sin(70°) = x/64

Simplifying the equation, we have: x = 64 * sin(70°)

Calculating the value of x, we get: x ≈ 60.771 m

Therefore, the ends of the raised parts of the bridge are approximately 60.771 meters apart when the bridge is fully opened.