Question

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

? \\(\text{ft}^2\\)

Explanation:

Identify the given values

$$ a = 4\text{ ft},\quad b = 10\text{ ft},\quad \theta = 37^\circ $$

Apply the sine area formula

$$ \text{Area} = \frac{1}{2} a b \sin(\theta) = \frac{1}{2} \cdot 4 \cdot 10 \cdot \sin(37^\circ) $$

Calculate and round the result

$$ \text{Area} = 20 \cdot \sin(37^\circ) \approx 20 \cdot 0.6018 = 12.036 \approx 12.0\text{ ft}^2 $$

Answer:

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

[ <blank>12.0</blank> ] \(\text{ft}^2\)