Question

triangle abc is a sketch of a triangular flower bed that has an area of 65.1 square feet. to the nearest foot, what amount of fencing is needed to surround the perimeter of the flower bed? trigonometric area formula: area = $\frac{1}{2}absin(c)$

Explanation:

Step1: Use area formula to find side b

$65.1 = \frac{1}{2} \times 10 \times b \times \sin(50^\circ)$

Step2: Solve for b

$\sin(50^\circ) \approx 0.7660$, so $65.1 = 5 \times b \times 0.7660 \implies b \approx 17$

Step3: Calculate perimeter

$13 + 10 + 17 = 40$

Answer:

40 feet