Solve for following applying spherical trigonometry... 1.Papua New Guinea (37° 45'N, 122°27'W)(since course was 260°) distance travelled =2250nm. A) use law of cosine to calculate a and thus altitude:or B) use law of sine to calculate N and thus longitude: or C) use law of ...
I think you have left out some important parts of the description.
To solve this problem using spherical trigonometry, we need to apply either the Law of Cosines or the Law of Sines. Let's go through both methods to calculate the necessary values.
A) Using the Law of Cosines:
1. Convert the given latitude and longitude values to radians.
latitude in radians = 37° 45'N = 37.75° = 37.75 * (π/180) radians
longitude in radians = 122°27'W = -122.45° = -122.45 * (π/180) radians
2. Calculate "a" using the Law of Cosines. In this case, "a" represents the angle between the starting point (Papua New Guinea) and the final destination.
a = 2250nm
3. Calculate the altitude using the formula: altitude = acos((cos(a) * cos(latitude)) - (sin(a) * sin(latitude) * cos(longitude)))
B) Using the Law of Sines:
1. Convert the given latitude and longitude values to radians (same step as above).
2. Calculate "N" using the Law of Sines. In this case, "N" represents the angle between the starting point (Papua New Guinea) and the meridian of the final longitude.
N = asin((sin(a) * sin(latitude)) / sin(latitude + altitude))
3. Calculate the final longitude using the formula: longitude = longitude + N
C) Using the Law of Tangents:
1. Convert the given latitude and longitude values to radians (same step as above).
2. Calculate "b" using the formula: b = atan2((sin(a) * cos(latitude)), (cos(a) * sin(latitude) * cos(longitude) - sin(latitude) * cos(a))))
3. Calculate the final longitude using the formula: longitude = longitude + b
Choose either method A, B, or C based on your preference or requirements, then apply the respective formulas to calculate the altitude or longitude.