Question

2 multiple choice 1 point. what is the area of µabc to the nearest tenth of a square meter? 200 in.² 169.0 in.² 84.5 in.² 93.3 in.²

Explanation:

Step1: Use the formula for the area of a triangle

The formula for the area of a triangle when two sides \(a\), \(c\) and the included angle \(A\) are known is \(S=\frac{1}{2}ac\sin A\). Here \(a = 20\), \(c=20\), and \(A = 25^{\circ}\).

Step2: Substitute the values into the formula

Substitute \(a = 20\), \(c = 20\), and \(A=25^{\circ}\) into the formula \(S=\frac{1}{2}\times20\times20\times\sin25^{\circ}\). First, calculate \(\frac{1}{2}\times20\times20=200\). Then, since \(\sin25^{\circ}\approx0.4226\), we have \(S = 200\times0.4226\).

Step3: Calculate the result

\(S=200\times0.4226 = 84.52\approx84.5\) (rounded to the nearest tenth).

Answer:

\(84.5\mathrm{in.}^2\) (the third option)