Question

find the area of this triangle.
round to the nearest tenth.
7 m
125°
14 m
? m²

Explanation:

Step1: Use 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 \(a = 7\), \(b = 14\), and \(C=125^{\circ}\).

Step2: Substitute the values into the formula

\(A=\frac{1}{2}\times7\times14\times\sin(125^{\circ})\). First, calculate \(\frac{1}{2}\times7\times14 = 49\). Then, \(\sin(125^{\circ})\approx0.8192\).

Step3: Calculate the area

\(A = 49\times0.8192=40.1408\).

Answer:

\(40.1\) \(m^{2}\)