A gap in a breakwater is 2 m wide. Water waves of wavelength 3 m strike the breakwater. At what angle is the first diffraction minimum?
A 20 degrees
B 50 degrees
C 15 degrees
D There is no diffraction minimum
E 25 degrees

I don't have time to help you now, but I answered a similar question some time ago. Please look at this and give it a shot:

https://www.askmehelpdesk.com/math-sciences/interference-physics-344109.html

Yeh but I used... angle = sin^-1(3/2) but gives me a domain error on my calc.. Hrmm?

The sine function gives an answer from -1 to +1. Sin^-1(3/2) is 1.5. Hence, the domain error. Show me your work and I'll try to figure out where you went wrong.

A gap in a breakwater is 2 m wide. Water waves of wavelength 3 m strike the breakwater. At what angle is the first diffraction minimum?
A 20 degrees
B 50 degrees
C 15 degrees
D There is no diffraction minimum
E 25 degrees


In single-slit diffraction, the following applies:

d\, sin(\theta) = m \lambda/math]

where λ is the wavelength and d is the width of the slit. M is the order of diffraction: 1,2,3, etc. We're looking for the case where m=1.

λ is 3 meters; d is 2 meters. This is the condition for a minimum with m=1

[math]sin(\theta) = \frac {3}{2}

Obviously we can't get arcsin(1.5) since you already tried it and it's obviously outside of the sine range. So either we did something wrong or there is no diffraction. No diffraction seems to be consistent with this:

http://hyperphysics.phy-astr.gsu.edu/HBASE/phyopt/fraungeo.html#c1

Plug the values in here, and it agrees -- no diffraction

http://hyperphysics.phy-astr.gsu.edu/HBASE/phyopt/sinslit.html#c1