Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. 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. image of the footbridge diagram 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 of the bridge length

The bridge is 20 feet long, and the diagonal supports meet at the center, so half the length is $\frac{20}{2} = 10$ feet.

Step2: Use cosine function in the right triangle

In the right triangle formed by the vertical support, half the bridge, and the diagonal support, we have $\cos(65^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}}=\frac{10}{x}$.

Step3: Solve for x

Rearranging the formula, we get $x = \frac{10}{\cos(65^\circ)}$. Calculating $\cos(65^\circ) \approx 0.4226$, so $x \approx \frac{10}{0.4226} \approx 23.7$.

Answer:

23.7