last team hmwk - Meghan Rees Whitney Hansley Alex Kaskel...

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Meghan Rees Whitney Hansley Alex Kaskel 6.7, #61 To solve problems a and b, Figure 6.90 is needed: a) D is the distance from the crow’s nest on the ship’s mast, point C, to the horizon, point H. The radius, r, forms a 90 ° angle with point H. We now have HCO. Using the Pythagorean Theorem, a 2 + b 2 = c 2 , where a and b are the two legs and c is the hypotenuse, we get the formula: d 2 + r 2 = (r+x) 2 r 2 +2rx+x 2 d 2 = 2rx + x 2 d = 2rx+x 2 The distance from the ship, S, to the horizon, H, along the Earth’s surface is represented by l. The angle from the center of the Earth, ϑ , is equal to the corresponding surface on the Earth, l. According to Sohcahtoa, sin = opposite . /. hypotenuse sin ( ϑ ) = d . /. (x+r) = l The radius is shown (twice) as a line from the center of the Earth, O, to the surface of the Earth, S and H. It is represented by r. Again, with HCO, we use the Pythagorean Theorem to get the formula: r 2 + d 2 = (r+x) 2 d 2 = 2xr + x 2 d 2 – x 2 = r 2x
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last team hmwk - Meghan Rees Whitney Hansley Alex Kaskel...

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