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Wislar
 2 years ago
Please help!
One side of a triangle is increasing at a rate of 3 cm/s and a second side is decreasing at a rate of 2 cm/s. If the area of the triangle remains constant, at what rate does the angle between the sides change when the first side is 20 cm long, the second side is 30 cm, and the angle is pi/6?
Wislar
 2 years ago
Please help! One side of a triangle is increasing at a rate of 3 cm/s and a second side is decreasing at a rate of 2 cm/s. If the area of the triangle remains constant, at what rate does the angle between the sides change when the first side is 20 cm long, the second side is 30 cm, and the angle is pi/6?

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experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1perhaps the Q meant this dw:1350751784378:dw

Wislar
 2 years ago
Best ResponseYou've already chosen the best response.0I thought this was related rates, but I'm in calc 3, and we are doing differentials and tangent approximations, so I'm kinda lost here. Plus, I don't really remember related rates too well

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1350751819497:dw yeah this is related rate.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1350751925717:dw

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1Given that \( {x = 20} , {dx \over dt} = 3 \) \( {y = 30} , {dy \over dt} = 2 \) \[ A = {1 \over 2} xy \; \sin \theta \\ {dA \over dt} = 0, \\ \text{Find } {d \theta \over dt }\]

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1If i interpreted the problem correctly ...

Wislar
 2 years ago
Best ResponseYou've already chosen the best response.0How did you get z=16.14?

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1forget that ... it's not necessary.

Wislar
 2 years ago
Best ResponseYou've already chosen the best response.0It's been along time since I've done related rates, so I may be wrong, but would I take the derivative of dA/dt first?

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1also given that \( \theta = {\pi \over 6} \) differentiate the above ... put the values and get the rest.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1Given area is constant ... dA/dt = 0

Wislar
 2 years ago
Best ResponseYou've already chosen the best response.0Would I differentiate A=.5 xysin(theta) ? What would I take the derivative with respect to?

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1time ... t, also you are given the values of dx/dt and dy/dt

Wislar
 2 years ago
Best ResponseYou've already chosen the best response.0dA/dt=.5 (dx/dt)ysin(theta)+x(dy/dt)sin(theta)+xy(theta)(cos(theta))(dtheta/dt) ?

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1yes ... put the values dA/dt = 0, all values are given, you only need to find the value of d(theta)/dt
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