Question

find the area of this triangle. round to the nearest tenth.

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, \(a = 8\), \(b=12\), and \(C = 62^{\circ}\).

Step2: Substitute the values into the formula

\(A=\frac{1}{2}\times8\times12\times\sin(62^{\circ})\). First, calculate \(\frac{1}{2}\times8\times12 = 48\). Then, find \(\sin(62^{\circ})\approx0.8829\).

Step3: Multiply the results

\(A = 48\times0.8829=42.3792\).

Answer:

\(42.4\)