Help!

[Asimov Pupil]

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.

[Kedas]

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.

[Sisyphus]

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.

[Kedas]

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

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

[Sisyphus]

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.

[Kedas]

Sorry I'm wrong forget that about the minus.

[Asimov Pupil]

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