Question

The towers of a suspension bridge reach 140m above the level of the bridge. The angles of elevation of the towers seen from the center the bridge and either end are 10 degrees and 19 degrees respectively. How long is the bridge?

Answer 1

To find the length of the bridge, we can use trigonometry and the angles of elevation provided. By using the tangent function, we can calculate the length of the bridge to be approximately 1570.84m.

Step-by-step explanation:

To find the length of the bridge, we can use trigonometry and the angles of elevation provided. Let's call the length of the bridge 'x'.

From the center of the bridge, we have a right triangle formed with the tower and the bridge. The angle of elevation of 10 degrees corresponds to the angle at the center of the bridge. Since the opposite side is the height of the tower and the adjacent side is half the length of the bridge, we can use the tangent function:

Tan(10°) = 140m / (x/2)

Simplifying, we get:

(x/2) = 140m / Tan(10°) = 785.42m

Multiplying both sides by 2, we find that the length of the bridge is approximately 1570.84m.