Questions: Find the area of this triangle. Round to the nearest tenth.

Solution Steps

The problem provides the following values:

• One side of the triangle (base) = 15 m
• Another side of the triangle = 12 m
• The angle between these two sides = 35°

The formula to find the area of a triangle when two sides and the included angle are known is: \[ \text{Area} = \frac{1}{2} \times a \times b \times \sin(C) \] where \( a \) and \( b \) are the sides, and \( C \) is the included angle.

Substitute \( a = 15 \) m, \( b = 12 \) m, and \( C = 35^\circ \) into the formula: \[ \text{Area} = \frac{1}{2} \times 15 \times 12 \times \sin(35^\circ) \]

Using a calculator, find \( \sin(35^\circ) \): \[ \sin(35^\circ) \approx 0.5736 \]

\[ \text{Area} = \frac{1}{2} \times 15 \times 12 \times 0.5736 \] \[ \text{Area} = \frac{1}{2} \times 15 \times 6.8832 \] \[ \text{Area} = \frac{1}{2} \times 103.248 \] \[ \text{Area} = 51.624 \]

Final Answer