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Question 1195838: 1.) F is the position of the sounding boat at the time a given sounding is made and E, C and D are the three shore points. EC = 1200m, CD = 965m, ∠ECD = 146°30’, ∠EFC = 28°15’ and ∠CFD = 22°30’. Find the distance DF.
2.) How far apart are two points on the equator one in longitude 40 degrees East and the other in longitude 150 degrees West?
3.) An airplane leaves Guam (13°24’ N, 114°38’ E) with an initial course of 36°40’ for a great-circle track. Locate the point of the great circle track which is nearest to the north pole.
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52873)   (Show Source):
You can put this solution on YOUR website! .
(2) How far apart are two points on the equator one in longitude 40 degrees East and the other in longitude 150 degrees West?
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Usually, such problems go with the given value for the Earth radius.
But, since the current problem is so special that does not give the value,
I will refer to this Wikipedia info https://en.wikipedia.org/wiki/Earth_radius
Earth radius (denoted as  ) is the distance from the center of Earth
to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid,
the radius ranges from a maximum of nearly 6,378 km (equatorial radius)
to a minimum of nearly 6,357 km (polar radius).
A nominal Earth radius is sometimes used as a unit of measurement in astronomy and geophysics,
which is recommended by the International Astronomical Union to be the equatorial value.
A globally-average value is usually considered to be 6,371 kilometres with a 0.3% variability (±10 km).
After this introduction, my solution is below.
One point is 40 degrees East along the equator from the zero meridian.
The other point is 150 degrees West along the equator from the zero meridian.
So, the central angle between these points is 40 + 150 = 190 degrees.
Since this angle is greater than 180 degrees, it is, obviously, the major central angle.
Since the question is about the distance between the points along the equator, we should take
a MINOR central angle, which complements 190 degrees to 360 degrees, i.e. 360-190 = 170 degrees.
Then the distance between the points is d =  = 18,894 kilometers
(rounded to the closest kilometer).
Solved.
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In your post, coordinates of Guam island in problem (3) are FATALLY INCORRECT.
In reality, they are TOTALLY different.
See Wikipedia, https://en.wikipedia.org/wiki/Guam
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! 2.) How far apart are two points on the equator one in longitude 40 degrees East and the other in longitude 150 degrees West?
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The distance given by Ikleyn is along the equator, which is probably what you expected.
But the distance between them is approximately the diameter of the Earth.
You should specify what distance you mean.
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