Answer:
The angle between Great Falls and Lemhi is approximately 3.02°
Step-by-step explanation:
The location parameters are;
The Great Falls location = 47.5° N, 111.3° W
The location of Lemhi = 45.5 °N and 113.5 °W
Therefore, we have;
The angle between the Great Falls and the poles, AP = 90° - 47.5° = 42.5°
The angle between Lemhi and the poles, PB = 90° - 45.5° = 44.5°
The angle between the lines of longitude, P = 113.5° - 113° = 0.5°
By the law of cosines for Sides of a spherical triangle, we have;
CosAB = cos AP·cosPB + sinAP·sinPB·cosP
Where;
AB = The angle between Great Falls and Lemhi
∴ CosAB = cos(47.5°) × cos(44.5°) + sin(47.5°) × sin(44.5°) × cos(0.5°) ≈ 0.9986
AB ≈ arccos(0.9986) ≈ 3.02°
The angle between Great Falls and Lemhi ≈ 3.02°
