Question

find the area of this triangle. round to the nearest tenth. 17 m 35° 15 m ?m²

Explanation:

Step1: Recall area formula

The area formula for a triangle with two - side lengths \(a\) and \(b\) and included - angle \(C\) is \(A=\frac{1}{2}ab\sin C\). Here \(a = 15m\), \(b = 17m\), and \(C = 35^{\circ}\).

Step2: Substitute values

Substitute \(a = 15\), \(b = 17\), and \(C = 35^{\circ}\) into the formula. We know that \(\sin35^{\circ}\approx0.574\). Then \(A=\frac{1}{2}\times15\times17\times\sin35^{\circ}\).
\[

$$\begin{align*} A&=\frac{1}{2}\times15\times17\times0.574\\ &=\frac{1}{2}\times15\times9.758\\ &=\frac{146.37}{2}\\ & = 73.185 \end{align*}$$

\]

Step3: Round the result

Round \(73.185\) to the nearest tenth. Since the hundredth - digit is 8 (\(> 5\)), we round up. So \(A\approx73.2m^{2}\).

Answer:

\(73.2\)