Question

trigonometry
progress.
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: Identify the trigonometric relationship

We know that $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, the length of the foot - bridge is the adjacent side to the $65^{\circ}$ angle and $x$ is the hypotenuse. The length of the foot - bridge is 25 feet and the angle $\theta = 65^{\circ}$. So, $\cos(65^{\circ})=\frac{25/2}{x}$ (since the two diagonal supports meet at the center of the 25 - foot bridge, the adjacent side for each right - triangle formed is $\frac{25}{2}$ feet).

Step2: Solve for $x$

We can re - arrange the formula $\cos(65^{\circ})=\frac{12.5}{x}$ to get $x=\frac{12.5}{\cos(65^{\circ})}$. We know that $\cos(65^{\circ})\approx0.4226$. Then $x=\frac{12.5}{0.4226}\approx29.6$.

Answer:

$29.6$