Question

find the area of this triangle. 65° 18 8 square units round to the nearest hundredth.

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 \(a = 8\), \(b=18\), and \(C = 65^{\circ}\).

Step2: Substitute the values into the formula

\(A=\frac{1}{2}\times8\times18\times\sin(65^{\circ})\). First, calculate \(\frac{1}{2}\times8\times18=72\). Then, find \(\sin(65^{\circ})\approx0.9063\).

Step3: Multiply the results

\(A = 72\times0.9063=65.2536\).

Answer:

\(65.25\)