Question

find the area of this triangle. round to the nearest tenth.

Explanation:

1. Recall the formula for the area of a triangle given two - sides and the included angle:

• The formula for the area of a triangle is \(A=\frac{1}{2}ab\sin C\), where \(a\) and \(b\) are the lengths of two sides of the triangle and \(C\) is the included angle between them.
• Let's assume the two given side - lengths are \(a = 15\) m and \(b = 17\) m, and the included angle \(C = 41^{\circ}\).

1. Substitute the values into the formula:

• First, we know that \(\sin(41^{\circ})\approx0.656\).
• Then, \(A=\frac{1}{2}\times15\times17\times\sin(41^{\circ})\).
• Calculate \(\frac{1}{2}\times15\times17=\frac{15\times17}{2}=\frac{255}{2}=127.5\).
• Now, \(A = 127.5\times\sin(41^{\circ})\).
• Substitute \(\sin(41^{\circ})\approx0.656\) into the equation: \(A\approx127.5\times0.656\).
• \(127.5\times0.656 = 83.64\).

1. Round the result:

• Rounding \(83.64\) to the nearest tenth gives \(83.6\) \(m^{2}\).

Step1: Identify the formula

Use \(A = \frac{1}{2}ab\sin C\).

Step2: Substitute values

\(A=\frac{1}{2}\times15\times17\times\sin(41^{\circ})\).

Step3: Calculate intermediate values

\(\frac{1}{2}\times15\times17 = 127.5\), \(\sin(41^{\circ})\approx0.656\).

Step4: Calculate the area

\(A = 127.5\times0.656=83.64\).

Step5: Round the result

Round \(83.64\) to \(83.6\).

Answer:

\(83.6\) \(m^{2}\)