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.

http://campus.northpark.edu/math/PreCalculus/Transcendental/Trigonometric/Geometry/

 

You will have to take the first derivative to 'the angle between them' of your solution. This will give you the ratio between the angle change and the lenght change.

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.

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

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

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.

Sorry I'm wrong forget that about the minus.

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