Question

find the area of \\( \triangle u v w \\).
write your answer as an integer or as a decimal rounded to the nearest tenth.
\\( \square \mathrm{km}^{2} \\)

Explanation:

Step1: Use the formula for the area of a triangle

The formula for the area of a triangle when two sides \(a\) and \(b\) and the included angle \(\theta\) is given is \(A=\frac{1}{2}ab\sin\theta\). Here, \(a = 19\), \(b = 40\), and \(\theta=40^{\circ}\).

Step2: Substitute the values into the formula

\(A=\frac{1}{2}\times19\times40\times\sin(40^{\circ})\)
First, calculate \(\frac{1}{2}\times19\times40\): \(\frac{1}{2}\times19\times40= 380\)
Then, find \(\sin(40^{\circ})\approx0.6428\)

Step3: Calculate the area

\(A = 380\times0.6428=244.264\approx244.3\)

Answer:

\(244.3\)