Question

find the area of this triangle. 7 95° 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 \(a = 7\), \(b=8\), and \(C = 95^{\circ}\).

Step2: Substitute the values into the formula

\(A=\frac{1}{2}\times7\times8\times\sin(95^{\circ})\). First, calculate \(\frac{1}{2}\times7\times8=28\). Then, since \(\sin(95^{\circ})\approx0.9962\) (using a calculator).

Step3: Calculate the area

\(A = 28\times0.9962=27.8936\)

Answer:

\(27.89\) square units