Question

find the area of \\( \triangle xyz \\).

write your answer as an integer or as a decimal rounded to the nearest tenth.

\\( \square \mathrm{mi}^{2} \\)

Explanation:

Step1: Recall the formula for the area of a triangle

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

Step2: Identify the values of \(a\), \(b\), and \(\theta\)

Here, \(a = 27\) mi, \(b = 47\) mi, and \(\theta=25^{\circ}\).

Step3: Substitute the values into the formula

$$
LATEXBLOCK0
$$

Answer:

\(269.3\ \text{mi}^2\)