Question

find the area of this triangle. round to the nearest tenth. 11 in 57° 6 in ? in²

Explanation:

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

The formula is \( A=\frac{1}{2}ab\sin C\), where \(a = 11\) in, \(b = 6\) in, and \(C = 57^{\circ}\).

Step2: Substitute the values into the formula

\(A=\frac{1}{2}\times11\times6\times\sin(57^{\circ})\)
First, calculate \(\frac{1}{2}\times11\times6=33\). Then, find \(\sin(57^{\circ})\approx0.8387\).

Step3: Multiply the results

\(A = 33\times0.8387=27.6771\)

Answer:

\(27.7\) in²