# Help!

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You have a triangle with two fixed sides of 12 and 15 meters. the angle between them is increasing at 2 Degrees per min. how fast is the opposite side increasing in length when the angle is 60 degrees?

i figure it's cos law but i don't know how to continue, or if it is even cos law.

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It is the law of cosines. Namely, c^2 = a^2 + b^2 + 2ab cosC, where a and b are the fixed sides, C is the increasing angle, and c is the increasing side. You know what a and b are, and so it becomes:

c^2 = 12^2 + 15^2 + 2(12)(15) cosC

simplified to

c^2 = 369 + 360cosC

or

c = sqrt(369 + 360cosC)

That can be rewritten as a function, with C as the independent variable and c as the dependent. Then you just take its derivative at C=60 to get the rate of change (increase in meters of c per degree of C). Since there is an increase of 2 degrees C per minute of time, just divide by two to get change in meters per minute.

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It's c² = a² + b² - 2ab cosC (notice the minus)

if C is increasing (0to90), cosC decreases, c is increasing.

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Oops. You shouldn't have said anything, though. If he didn't know it was wrong, he could have learned a valuable lesson about accepting magical equations from nowhere without seeing where they come from.

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Sorry I'm wrong forget that about the minus.

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Thanks I think my main problem though was mixing up the sin and cos Laws! thanks a million!!!!

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