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 25-foot-long footbridge has two diagonal supports that meet in the center of the bridge.each support makes a $65^\circ$ angle with a short vertical support.what is the length $x$ of a diagonal support, to the nearest tenth of a foot?$x \approx$ _______ feetthe solution is

Explanation:

Step1: Find half the bridge length

The bridge is 25 ft long, so half its length is $\frac{25}{2} = 12.5$ ft.

Step2: Use cosine to solve for x

The horizontal segment (12.5 ft) is adjacent to the $65^\circ$ angle, and $x$ is the hypotenuse. Use $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$.
Rearrange to solve for $x$:
$x = \frac{12.5}{\cos(65^\circ)}$
Calculate $\cos(65^\circ) \approx 0.4226$, so:
$x \approx \frac{12.5}{0.4226} \approx 29.6$

Answer:

$x \approx 29.6$ feet
The solution is $\boldsymbol{29.6}$