Question

Calculus: rate of change
Two sides of a triangle have lengths 12m and 12m. The angle between them is increasing at a rate of 2 degrees per minute. How fast is the length of the third side increasing when the angle between the sides of fixed length is 60 deg.?

Answer 1

law of cosines should be useful for this

Answer 2

\[c^2=a^2+b^2-2ab~\cos(\alpha)\]
\[2cc'=2aa'+2bb'-2ab'~\cos(\alpha)-2a'b~\cos(\alpha)-2ab\alpha'~\sin(\alpha)\]
\[cc'=aa'+bb'-ab'~\cos(\alpha)-a'b~\cos(\alpha)-ab\alpha'~\sin(\alpha)\]
since a' and b' are not changing, they equal 0
\[cc'=-ab\alpha'~\sin(\alpha)\]
\[c'=-\frac{ab}{c}\alpha'~\sin(\alpha)\]

Answer 3

i think i got a bad negative during that lol

Answer 4

a,b,c = 12; alpha=60, alpha'=2

\[c'=\frac{12(12)}{12}2~\sin(60)\]
\[c'=24\sin(60)\]

Answer 5

does that make sense?

Answer 6

step by step checking it out.........

Answer 7

c' =ab/c sine x....yes, but where do you get c=12?

Answer 8

when the angle is 60 degrees, you have an equilateral triangle ...

Answer 9

Oh my goodness........I knew that!
Thanks