Question

find the area of this triangle. round to the nearest tenth. 24 in 11 in 76° 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 \(a\) and \(b\) are the lengths of two sides and \(C\) is the included angle. Here, \(a = 24\) in, \(b=11\) in, and \(C = 76^{\circ}\).

Step2: Substitute the values into the formula

\(A=\frac{1}{2}\times24\times11\times\sin(76^{\circ})\)
First, \(\frac{1}{2}\times24\times11= 132\). Then, \(\sin(76^{\circ})\approx0.9703\)

Step3: Calculate the area

\(A = 132\times0.9703=128.0796\)

Answer:

\(128.1\)