I am having problems with the following question:
"The area of a triangle ABC is calculated using the formula:
and it is known that b, c and A are measured correctly to within 1%. If the angle A is measured as 45 degrees, prove that the percentage error in the calculated value of S is not more than about 2.8%."
When I use the equation:
(delta)S= (dS/db)(delta b) + (dS/dc)(delta c) + (dS/dA)(delta A)
and subsequently divide by S, I get:
(delta)S/S= (delta)b/b + (delta)c/c + (cosA/sinA)(delta A)
and at this point I am totally stuck. What happens to the delta A here? And for the cosA/sinA do I use angle A as 45 degrees?
Any help would be fantastic.