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? the solution is x ≈ feet

Explanation:

Step1: Use trigonometric relation

We know that $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 65^{\circ}$ and the opposite - side to the $65^{\circ}$ angle is half of the height of the foot - bridge (since the two diagonal supports meet in the center), which is $\frac{25}{2}=12.5$ feet, and the hypotenuse is $x$.
So, $\sin65^{\circ}=\frac{12.5}{x}$.

Step2: Solve for $x$

We can re - arrange the equation $\sin65^{\circ}=\frac{12.5}{x}$ to get $x=\frac{12.5}{\sin65^{\circ}}$.
We know that $\sin65^{\circ}\approx0.9063$. Then $x=\frac{12.5}{0.9063}\approx13.8$.

Answer:

$13.8$