Question

a 25-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 the bridge length

Half of 25 feet is $\frac{25}{2} = 12.5$ feet. This is the adjacent side of the right triangle formed by the diagonal support, vertical support, and half the bridge.

Step2: Use cosine to find x

The cosine of 65° equals adjacent over hypotenuse: $\cos(65^\circ) = \frac{12.5}{x}$. Rearrange to solve for x: $x = \frac{12.5}{\cos(65^\circ)}$.

Step3: Calculate the value

$\cos(65^\circ) \approx 0.4226$, so $x \approx \frac{12.5}{0.4226} \approx 29.6$.

Answer:

29.6