Derivatives of Trig with Triangles

[LadiesMan]

[SOLVED] Derivatives of Trig with Triangles

1. Two sides of a triangle are six and eight metres in length. If the angle between them decreases at the rate of 0.035 rad/s, find the rate at which the area is decreasing when the angle between the sides of fixed length is pi/6. Answer 0.727 m^2/min


2. I tried using Heron's formula but I realized it was almost impossible to take the derivative somehoe with the angle needed. My givens are
dtheta/dt = -0.035 rad/s
the angle between them is pi/6 or 30 degrees
Now to find da/dt...

Thanks

 

[belliott4488]

I'm not sure why you're using Heron's formula - that looks to be better when you know all three sides and don't necessarily know any of the angles.

Can you express the area as a function of the two fixed lengths and the contained angle? It's pretty simple to take the derivative of the relevant expression.

 

[LadiesMan]

no sry i don't understand how to express the equation but what i think is cut the triangle into two?

 

[LadiesMan]

nvmi got it thank you very much! =) But one thing when u take the derivative of 24sin theta,w hy is it that u leave the 24?

 

[belliott4488]

I'm not sure I understand your question. It's just:

d/dt (k*f(t)) = k* df/dt , k = constant

Is that clear?