Question

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

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

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

Explanation:

Step1: Recall 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 \(\theta\) are known is \(A=\frac{1}{2}ab\sin\theta\).

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

Here, \(a = 48\ \text{cm}\), \(b=19\ \text{cm}\), and \(\theta = 47^{\circ}\).

Step3: Substitute the values into the formula

\(A=\frac{1}{2}\times48\times19\times\sin(47^{\circ})\).
First, calculate \(\frac{1}{2}\times48\times19 = 456\).
Then, find \(\sin(47^{\circ})\approx0.7314\).

Step4: Calculate the area

\(A = 456\times0.7514\approx342.9\ \text{cm}^2\).

Answer:

$342.9\ \text{cm}^2$