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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




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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