Question

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

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 by \(A=\frac{1}{2}ab\sin\theta\). Here, \(a = 15\), \(b=17\), and \(\theta = 35^{\circ}\).

Step2: Substitute the values into the formula

Substitute \(a = 15\), \(b = 17\), and \(\theta=35^{\circ}\) into the formula \(A=\frac{1}{2}ab\sin\theta\).

$$
LATEXBLOCK0
$$

We know that \(\sin(35^{\circ})\approx0.5736\).

$$
LATEXBLOCK1
$$

Step3: Round the result

Round \(73.134\) to the nearest tenth. Since the digit in the hundredth place is \(3\lt5\), we keep the digit in the tenth place as it is.

Answer:

\(73.1\)