To find the area of a spherical triangle with three right angles on a sphere, we can use the following formula:
Area = (r^2) * (A + B + C - π)
where:
r is the radius of the sphere,
A, B, and C are the angles of the spherical triangle in radians,
π is a mathematical constant approximately equal to 3.14159.
Since the triangle has three right angles, each angle (A, B, C) is equal to π/2 radians.
Substituting the given values into the formula:
Area = (1950^2) * ((π/2) + (π/2) + (π/2) - π)
Simplifying the expression:
Area = (1950^2) * (3π/2 - π)
Calculating the area using this expression will give us the approximate area of the spherical triangle. Let's perform the calculation and round the result to the nearest ten thousand square miles.