gettin’ mathy with it

friday at the mission is a defacto half day, so we came back to the hotel just after noon, and sat out by the pool reading and watching the ocean.

which makes me wonder how far out can i actually see, how far away is that boat on the very edge of the horizon?

pythagorean theorem diagram

with a little help from the pythagorean theorem and the interweb, i figured that if i was standing on the shoreline, i’d probably be able to see about 3 miles. hotel sea cliff just happens to be perched on a cliff (on the sea), so i can’t exactly stand at the shoreline, but assuming the cliff is about 40 feet off the water, i can probably see over 7 miles to the horizon.

i even made a cute little diagram:

diagram plotting distance to horizon

solving for b:
a2 + b2 = (a + c)2
a2 + b2 = a2 + 2ac + c2
b2 = 2ac + c2
b= √(2ac + c2)

oh, and it helps to know there are 5280 feet in a mile

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