Problem $4(15$pts$)$:

a$)$ A shore$-$parallel semi$-$infinite rigid impermeable breakwater has been built in $4\mathrm{.}5$ m water depth to

protect boats anchored in a marina. The breakwater extends eastward from its tip. The most critical

design conditions have been measured at the tip of the breakwater and consist of waves with a height

of $1\mathrm{.}3$ m and a period of $9$ s approaching the breakwater from the south$-$east at an angle of $15($angle

between wave crests and breakwater$).$ Assuming straight and parallel contours of the offshore

bathymetry, calculate the deepwater wave height and angle based on shoaling and refraction only.

Include a sketch of the situation and show all calculation steps.

b$)$ The wave is now diffracted by the breakwater. The water depth inside the marina is constant at $4\mathrm{.}5$

m $.$ Find the wave height $H_D$ at a location inside the marina with polar coordinates