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Sinusoidal functions of the elevation of the sun vs. time????
if we have the following assumptions...
a) on the 20th march 2009 (vernal equinox) the sun spends and equal amount of time above the horizon as it does below the horizon.
b) its maximum elevation above the horizon is 62.5degrees at midday.
c) the function for elevation of the sun verses time is sinusoidal
is someone able to determine a function to model sun elevation (in degrees) verses the time (in days) for the 20th of march 2009?
can someone please assist me?
One general sinusoidal function is y = Asin(Bx + C) + D.
'A' is the amplitude, which is 62.5º.
The period is 24 hours, and B = 2π/period = 2π/24 = π/12.
D is the vertical shift (from y = sin(x)), which is zero.
Plugging those values in gives :
y = 62.5sin[(π/12)x + C]
Now let's take a point on the graph.
Maximum elevation is 62.5º at midday (12 hours), so let x = 12 and y = 62.5.
Plugging those in gives :
62.5 = 62.5sin[(π/12)(12) + C]
Therefore, sin(π + C) = 1 = sin(π/2)
π + C = π/2
C = -π/2
The equation is thus : y = 62.5sin[(π/12)x - π/2]
And I hope you mean time in hours rather than days!
Some values of the function :
x = 00:00 hr. (midnight) implies y = -62.5º (minimum)
x = 06:00 hr. implies y = 0º (sun on horizon)
x = 12:00 hr. (midday) implies y = 62.5º (maximum)
x = 18:00 hr. implies y = 0º (sun on horizon)
x = 24:00 hr. (midnight) implies y = -62.5 (minimum) (after 1 full cycle)
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Elevation Certificates FEMA Standards Tampa, FLorida
Need help with right angle triangle?
I have a question on right angle triangles.
While traveling across flat land, you notice a mtn. directly in front of you. The angle of elevation to the peak is 38 deg. After you travel 1900 ft closer to the mtn. the angle of elevation is 51 degrees. Appr. the height of the4 mountain.
I don't understand how to translate the 1900 ft. closer to the mountain into a side measurement. If someone could assist in explaining how to finish the problem it would be greatly appreciated. I understand how to get the three angles, how to get the sides is what is baffling me.
Please and Thank you
Thanks Carolyn but I need help by tomorrow morning.
Thank you so much I get it now.
You will have two right triangles that share the upright leg representing the mountain. The 1900 is the distance from the bottom leg end of the smaller triangle to the bottom leg end of the bigger overlapping right triangle. The bottom leg of the smaller right triangle is x, and the bottom of the big triangle is therefore x + 1900. So, assuming you don't know the law of cosines, you use tangent of each triangle to get 2 equations (h = height of mountain):
tan 51 = h/x
tan 38 = h/(x + 1900)
so you solve that system of equations
good luck, email or IM if you want to discuss it more
