Final answer:
To find the area of a spherical triangle ABN on Earth, use the spherical excess formula by measuring the angles at each vertex and use the radius of the Earth (half of the diameter) in the area calculation formula.
Step-by-step explanation:
The area of a spherical triangle on Earth can be determined using the spherical excess formula, which takes into account the Earth's radius and the angles at each vertex of the triangle.
The formula is E = A + B + C - π, where E is the spherical excess in radians, and A, B, and C are the angles at the vertices. Given that the radius of the Earth is half the diameter, which is 3956 miles, we calculate the area of the spherical triangle by Area = E * r², where r is the radius of the Earth in miles
. To find the area, you'll need to measure or be given the angles of the spherical triangle in radians and substitute these, along with the Earth's radius, into the above formulas.