Answer:
dA/dt = 0.375√3 ft² ≈ 0.6495 ft²/s
Step-by-step explanation:
The area is given by the formula ...
A = (1/2)ab·sin(C)
where a and b are side lengths, and C is the angle between them. Differentiating, we have ...
dA/dt = (1/2)ab·cos(C)·dC/dt
Filling in the given information, we get ...
dA/dt = (1/2)(3 ft)(5 ft)(cos(π/6))(0.1 rad/s) = 0.75(√3)/2 ft²/s
dA/dt = 0.375√3 ft² ≈ 0.6495 ft²/s
