Question

finding area find the area of the figure. round decimal answers to the nearest tenth. 25. 60° 12 ft

Explanation:

Step1: Identify right triangle sides

This is a right triangle with hypotenuse $c=12$ ft, one angle $60^\circ$.
Find adjacent side (to $60^\circ$):
$a = c \cdot \cos(60^\circ) = 12 \cdot 0.5 = 6$ ft
Find opposite side (to $60^\circ$):
$b = c \cdot \sin(60^\circ) = 12 \cdot \frac{\sqrt{3}}{2} = 6\sqrt{3}$ ft

Step2: Calculate triangle area

Use area formula $\frac{1}{2} \times base \times height$
$\text{Area} = \frac{1}{2} \times a \times b$
$\text{Area} = \frac{1}{2} \times 6 \times 6\sqrt{3} = 18\sqrt{3}$

Step3: Convert to decimal, round

$18\sqrt{3} \approx 18 \times 1.732 = 31.176$
Round to nearest tenth: $31.2$

Answer:

$31.2$ square feet