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° 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 the length of the base of the right - triangle

Since the footbridge is 25 feet long and the diagonal supports meet in the center, the base of the right - triangle formed by the diagonal support, the vertical support, and half of the footbridge is \(b=\frac{25}{2}=12.5\) feet.

Step2: Use the sine function

We know that \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 65^{\circ}\), the opposite side to the \(65^{\circ}\) angle is the base of the right - triangle (\(b = 12.5\) feet), and the hypotenuse is the diagonal support \(x\).
So, \(\sin65^{\circ}=\frac{12.5}{x}\).

Step3: Solve for \(x\)

We can rewrite the equation as \(x=\frac{12.5}{\sin65^{\circ}}\).
Since \(\sin65^{\circ}\approx0.9063\), then \(x=\frac{12.5}{0.9063}\approx13.8\)

Answer:

\(13.8\)