The law of cosines for a triangle can be written a^2= b^2+ c^2? 2bc cos ?. At ti

Question

The law of cosines for a triangle can be written

a^2= b^2+ c^2? 2bc cos ?.

At time t0 we have b0 = 10 inches, c0 = 15 inches, ?0 =13Pi radians.

(a) Find a0.
(b) Find the rate of change of a with respect to b at time t0 given that c and ? remain constant.
(c) Using the rate found in part (b), calculate (by differentials) the approximate change in a if b is decreased by 1 inch.
(d) Find the rate of change of a with respect to ? at time t0 given that b and c remain constant.
(e) Find the rate of change of c with respect to ? at time t0 given that a and b remain constant.

Explanation / Answer

a)a0=325+(2*150*cos(13pi))=25 b)the value is [b0+c0*cos(13pi)]/a0 =-0.2 c)0.24 d) the solution is [-2*b*c*sin(13pi)]/a=0 e)0.2

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