Question

a 20 - foot - long footbridge has two diagonal supports that meet in the center of the bridge. each support makes a 65° angle with a short vertical support. what is the length x of a diagonal support, to the nearest tenth of a foot? x ≈ ______ feet the solution is

Explanation:

Step1: Find half-bridge length

The bridge is 20 ft, so half is $20/2 = 10$ ft.

Step2: Relate angle to sides

In right triangle, $\sin(65^\circ) = \text{opposite}/\text{hypotenuse} = 10/x$.

Step3: Solve for x

$x = 10/\sin(65^\circ) \approx 10/0.9063 \approx 11.03$.

Step4: Round to nearest tenth

$x \approx 11.0$.

Answer:

11.0