Question

find the area of this triangle. round to the nearest tenth. 12 cm 33° 5.5 cm ? cm²

Explanation:

Step1: Recall area formula for a triangle

The formula for the area of a triangle with two - side lengths \(a\) and \(b\) and included angle \(\theta\) is \(A=\frac{1}{2}ab\sin\theta\). Here \(a = 12\) cm, \(b = 5.5\) cm and \(\theta=33^{\circ}\).

Step2: Substitute values into the formula

\(A=\frac{1}{2}\times12\times5.5\times\sin(33^{\circ})\). First, calculate \(\sin(33^{\circ})\approx0.5446\). Then \(\frac{1}{2}\times12\times5.5\times0.5446 = 6\times5.5\times0.5446\).

Step3: Perform the multiplication

\(6\times5.5\times0.5446=33\times0.5446 = 17.9718\) \(cm^{2}\).

Step4: Round to the nearest tenth

Rounding \(17.9718\) to the nearest tenth gives \(18.0\) \(cm^{2}\).

Answer:

\(18.0\) \(cm^{2}\)