Question

the area of triangle efg is 34.8 square units. what is the perimeter of triangle efg to the nearest unit?
29 units
30 units
41 units
60 units
trigonometric area formula: area = $\frac{1}{2}absin(c)$

Explanation:

Step1: Identify known values

Area=34.8, angle=56°, sides: assume FE=12, FG=x (included angle 56°)

Step2: Apply area formula to find FG

$34.8 = \frac{1}{2} \times 12 \times x \times \sin(56^\circ)$

Step3: Solve for x (FG)

$x = \frac{34.8 \times 2}{12 \times \sin(56^\circ)} \approx \frac{69.6}{12 \times 0.8290} \approx 7$

Step4: Calculate perimeter

Perimeter = 10 + 12 + 7 = 29

Answer:

A. 29 units