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: Find half - length of bridge

The bridge is 20 feet long, so half - length is $\frac{20}{2}=10$ feet.

Step2: Use cosine function

We know $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here $\theta = 65^{\circ}$ and adjacent side to the angle is 10 feet. So $\cos65^{\circ}=\frac{10}{x}$.

Step3: Solve for x

$x=\frac{10}{\cos65^{\circ}}\approx\frac{10}{0.4226}\approx23.7$

Answer:

23.7