Question

find the area of this triangle. round to the nearest tenth. 4 ft 37° 10 ft ? ft²

Explanation:

Step1: Recall the formula for the area of a triangle with two sides and included angle

The formula for the area of a triangle when two sides \(a\) and \(b\) and the included angle \(\theta\) is given is \(A=\frac{1}{2}ab\sin\theta\). Here, \(a = 4\) ft, \(b=10\) ft, and \(\theta = 37^{\circ}\).

Step2: Substitute the values into the formula

Substitute \(a = 4\), \(b = 10\), and \(\theta=37^{\circ}\) into the formula \(A=\frac{1}{2}ab\sin\theta\). We know that \(\sin(37^{\circ})\approx0.6018\). So \(A=\frac{1}{2}\times4\times10\times\sin(37^{\circ})\).
First, calculate \(\frac{1}{2}\times4\times10 = 20\). Then \(A = 20\times0.6018\).

Step3: Calculate the value

\(A=20\times0.6018 = 12.036\).

Answer:

\(12.0\)