Question

what is the area of the triangle? round your answer to the nearest tenth.
area = square units

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 \(a\), \(b\) and the included angle \(\theta\) is given by \(A=\frac{1}{2}ab\sin\theta\). Here, \(a = 11\), \(b=19\), and \(\theta = 64^{\circ}\).

Step2: Substitute the values into the formula

Substitute \(a = 11\), \(b = 19\), and \(\theta=64^{\circ}\) into \(A=\frac{1}{2}ab\sin\theta\). So, \(A=\frac{1}{2}\times11\times19\times\sin(64^{\circ})\).
First, calculate \(\frac{1}{2}\times11\times19=\frac{209}{2}=104.5\).
Then, find \(\sin(64^{\circ})\approx0.8988\).

Step3: Calculate the area

Multiply the two results: \(A = 104.5\times0.8988\).
\(A=104.5\times0.8988 = 94.0246\)

Answer:

\(94.0\) square units