Question

the campground at a park is designed in a triangular fashion, surrounded on all three sides by trails. the property has 45 feet of frontage on one trail, and 38 feet of frontage on another; these two trails intersect at a 61° angle. what is the square footage of the attraction? round to the nearest hundredth.

Explanation:

Step1: Recall the area formula for a triangle

The formula for the area of a triangle when two - side lengths $a$ and $b$ and the included angle $C$ are given is $A=\frac{1}{2}ab\sin C$.

Step2: Identify the values of $a$, $b$ and $C$

Let $a = 45$ feet, $b = 38$ feet and $C=61^{\circ}$.

Step3: Calculate the area

First, find the value of $\sin(61^{\circ})\approx0.8746$. Then, substitute the values into the formula:

$$
LATEXBLOCK0
$$

Rounding to the nearest hundredth, $A\approx747.78$ square - feet.

Answer:

$747.78$