1. ## solving help required

hi.

A*sin(atan(2000/B)*2) = 500
A*sin(atan(4000/B)*2) = 752.545

and explain it.

thanks
mohanraj

2. to add to that, by dividing the equation and by substitution method, we can find the value, but i dont know how to solve the equations.

3. Originally Posted by sanmo4
hi.

A*sin(atan(2000/B)*2) = 500
A*sin(atan(4000/B)*2) = 752.545

and explain it.

thanks
mohanraj
Umm, big numbers.

You know that arctan(U) is an angle.
It is an angle whose tan value is U.
So, in its reference triangle,
opposite side = U
hypotenuse = sqrt(1 +U^2)
And then, sin(arctan(U)) = opp/hyp = U /sqrt(1 +U^2)
And, cos(arctan(U)) = adj/hyp = 1 /sqrt(1 +U^2)

To avoid plunging into very large numbers at once, let
arctan(2000/B) = angle X
arctan(4000/B) = angle Y

Thus, the original equations can be re-written as:
A*sin(2X) = 500 ---------(1a)
A*sin(2Y) = 752.545 ------(2a)

A[2sinXcosX] = 500 ---------(1b)
A[2sinYcosY] = 752.545 -----(2b)

To eliminate A, divide (1b) by (2b)
sinXcosX /sinYcosY = 0.664412 -------------(3)

Use the method in the sample U above and you'd get
sinX = 2000 /sqrt(B^2 +4,000,000)
cosX = B /sqrt(B^2 +4,000,000)

sinY = 4000 /sqrt(B^2 +16,000,000)
cosY = B /sqrt(B^2 +16,000,000)

Substitute those into Eq.(3)
Etc....

You should get B = 5700
And A = 800