Question

find the area of this triangle. round to the nearest tenth. 10 cm 55° 12 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 the included angle \(C\) is \(A=\frac{1}{2}ab\sin C\). Here, \(a = 10\mathrm{cm}\), \(b = 12\mathrm{cm}\), and \(C = 55^{\circ}\).

Step2: Substitute the values into the formula

\(A=\frac{1}{2}\times10\times12\times\sin(55^{\circ})\).
First, calculate \(\frac{1}{2}\times10\times12 = 60\). Then, find \(\sin(55^{\circ})\approx0.819\).

Step3: Calculate the area

\(A = 60\times0.819=49.14\mathrm{cm}^{2}\).

Step4: Round to the nearest tenth

Rounding \(49.14\) to the nearest tenth gives \(49.1\mathrm{cm}^{2}\).

Answer:

\(49.1\mathrm{cm}^{2}\)