A submarine is $2\mathrm{.}76102$ m horizontally from shore and $1\mathrm{.}00102$ m beneath the surface of the water. A laser beam is sent from the submarine so that the beam strikes the surface of the water $2\mathrm{.}48102$ m from the shore. A building stands on the shore, and the laser beam hits a target at the top of the building. The goal is to find the height of the target above sea level.

$($a$)$ Draw a diagram of the situation, identifying the two triangles that are important to finding the solution.

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$($b$)$ Find the angle of incidence of the beam striking the water$-$air interface.

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$($c$)$ Find the angle of refraction. $($Use $1\mathrm{.}333$ as the index of refraction for water.$)$

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$($d$)$ What angle does the refracted beam make with respect to the horizontal?

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$($e$)$ Find the height of the target above sea level.

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