Question

a 50 foot rope on a dock is connected to a boat at a 35° angle with the boat. how far away is the boat from the dock? round your answer to the nearest hundredth.

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle situation where the rope is the hypotenuse ($c = 50$ feet) and we want to find the adjacent side ($x$) to the given angle ($\theta=35^{\circ}$). The cosine function is defined as $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, so $x = c\times\cos\theta$.

Step2: Substitute the values

Substitute $c = 50$ and $\theta = 35^{\circ}$ into the formula. We know that $\cos(35^{\circ})\approx0.8192$. Then $x=50\times\cos(35^{\circ})$.

$$x = 50\times0.8192$$

$$x=40.96$$

Answer:

$40.96$