Question

find the area of this triangle. round to the nearest tenth. 9 ft 20 ft 110° 15 ft ?ft²

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 \(\theta\) is \(A=\frac{1}{2}ab\sin\theta\).

Step2: Identify \(a\), \(b\), and \(\theta\)

Let \(a = 9\) ft, \(b = 15\) ft, and \(\theta=110^{\circ}\).

Step3: Calculate the area

First, find the value of \(\sin(110^{\circ})\approx0.9397\). Then, substitute the values into the formula: \(A=\frac{1}{2}\times9\times15\times\sin(110^{\circ})\).
\[

$$\begin{align*} A&=\frac{1}{2}\times9\times15\times0.9397\\ &=\frac{1}{2}\times135\times0.9397\\ & = 67.5\times0.9397\\ &\approx63.5 \end{align*}$$

\]

Answer:

\(63.5\)