Question

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

Explanation:

Step1: Recall the formula for the area of a triangle with two sides and included angle

The formula for the area of a triangle when two sides \(a\) and \(b\) and the included angle \(\theta\) is given by \(A=\frac{1}{2}ab\sin\theta\). Here, \(a = 50\) yd, \(b=22\) yd, and \(\theta = 42^{\circ}\).

Step2: Substitute the values into the formula

Substitute \(a = 50\), \(b = 22\), and \(\theta=42^{\circ}\) into \(A=\frac{1}{2}ab\sin\theta\). So, \(A=\frac{1}{2}\times50\times22\times\sin(42^{\circ})\).
First, calculate \(\frac{1}{2}\times50\times22\): \(\frac{1}{2}\times50\times22= 50\times11=550\).
Then, find \(\sin(42^{\circ})\approx0.66913\).

Step3: Calculate the area

Multiply the results: \(A = 550\times0.66913\).
\(A=550\times0.66913 = 368.0215\approx368.0\) (rounded to the nearest tenth).

Answer:

\(368.0\)