Question

a 20 - 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: Determine the base - length of the right - triangle

The footbridge is 20 feet long and the diagonal supports meet in the center. So the base - length of the right - triangle formed by the diagonal support, the vertical support, and half of the footbridge is $\frac{20}{2}=10$ feet.

Step2: Use trigonometry to find the length of the diagonal support

We know that $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 65^{\circ}$ and the adjacent side to the $65^{\circ}$ angle is 10 feet, and the hypotenuse is $x$. So $\cos65^{\circ}=\frac{10}{x}$.
We can rewrite the equation as $x=\frac{10}{\cos65^{\circ}}$.
Since $\cos65^{\circ}\approx0.4226$, then $x=\frac{10}{0.4226}\approx23.66$.

Answer:

$23.7$