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? ( xapprox ) feet the solution is

Explanation:

Step1: Find the length of the base of one right - triangle

Since the footbridge is \(25\) feet long and the diagonal supports meet in the center, the base of one right - triangle is \(\frac{25}{2}=12.5\) 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 \(12.5\) feet, and the hypotenuse is \(x\). 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:

\(13.8\)