Wavelength of the red colour of this helium discharge tube

[songoku]

Homework Statement

A grating spectrometer is used to view the spectrum of light from a helium discharge tube. Three brightest spectral lines seen are blue, red and yellow. These lines appear at positions A, B and C in the figure but not necessarily in that order. The distance between the grating and screen is 30 cm and the slit spacing in the grating is 1870 nm. What is the wavelength of red colour?
a. 767 nm
b. 398 nm
c. 669 nm
d. 565 nm
e. 454 nm

Relevant Equations

x = λ.L / d

x = fringe separation
L = distance between grating and screen
d = slit spacing

Red has the longest wavelength compared to the two other colours so the location of red will be at point C.

x = 11.5 cm
L = 30 cm
d = 1870 nm

Putting all into the formula, I get λ = 717 nm

Where is my msitake?

Thanks

 

[TSny]

Relevant Equations:: x = λ.L / d

This equation is valid only for small angles $\theta$.

 

[songoku]

is d sin θ = nλ the formula I need to use?

 

[TSny]

is d sin θ = nλ the formula I need to use?

Yes

 

[songoku]

Thank you very much for the help TSny