Question

find the area of this triangle. 123° 15 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 \(a = 15\), \(b=8\), and \(C = 123^{\circ}\).

Step2: Substitute the values into the formula

\(A=\frac{1}{2}\times15\times8\times\sin(123^{\circ})\). First, calculate \(\frac{1}{2}\times15\times8=60\). Then, find \(\sin(123^{\circ})\approx0.8387\) (using a calculator in degree mode).

Step3: Multiply the results

\(A = 60\times0.8387=50.322\)

Answer:

\(50.32\) square units