Okay so I've been at this for quite a while now and just need some help.
Here's a description on what the problem is about:
Lewis and Clark followed several rivers in their trek from what is now Great Falls, Montana, to the Pacific coast. First, they went down the Missouri and Jefferson rivers from Great Falls to Lemhi, Idaho. Because the two cities are on different longitudes and different latitudes, we must account for the curvature of the Earth when computing they traveled. Assume the radius of Earth is 3960.
Here's the problem:
Great Falls is a approximately 47.5 degrees N, and 111.3 degrees W. Lemhi is approx 45.5 degrees N, and 113.5 degrees W. (Assuming that the rivers flow straight from Great Falls to Lemhi on the surface of Earth). Apply the Law of Sides of a spherical triangle to find the angle between Great Falls and Lemhi. Then find the length of the arc length joining Great Falls and Lemhi. (Note: Assume radius is 3960. s=θr, where θ is in radians)
Here's what I have so far (which isn't much but please bear with me):
So far I have figured out 2 sides and 1(?) angle:
S2= 42.5 (Found by subtracting the first latitude (47.5) from 90 degrees)
S3= 44.5 (Found by subtracting the second latitude (45.5) from 90 degrees)
a1=2.2 (Found by subtracting the longitudes (111.3 and 113.5) from each other)
Now, I'm trying to find the angle between Great Falls and Lemhi.
To do this, S1 would be needed, right?
To do that I used this formula: cos(S1)=cos(S2)*cos(S3)+sin(S2)*sin(S3)*cos(a1)
I plugged in my numbers a few times and couldn't seem to get a number that made sense, but eventually I came up with 44.9. Is that right? S1=44.9??
And this is where I'm not sure what to do from here. How do I find the angle between GF and Lemhi and how do I find the arc length joining the two?
(TL;DR) 1. How do I find the angle between Great Falls and Lemhi and 2. how do I find the arc length joining Great Falls and Lemhi?
Here's a description on what the problem is about:
Lewis and Clark followed several rivers in their trek from what is now Great Falls, Montana, to the Pacific coast. First, they went down the Missouri and Jefferson rivers from Great Falls to Lemhi, Idaho. Because the two cities are on different longitudes and different latitudes, we must account for the curvature of the Earth when computing they traveled. Assume the radius of Earth is 3960.
Here's the problem:
Great Falls is a approximately 47.5 degrees N, and 111.3 degrees W. Lemhi is approx 45.5 degrees N, and 113.5 degrees W. (Assuming that the rivers flow straight from Great Falls to Lemhi on the surface of Earth). Apply the Law of Sides of a spherical triangle to find the angle between Great Falls and Lemhi. Then find the length of the arc length joining Great Falls and Lemhi. (Note: Assume radius is 3960. s=θr, where θ is in radians)
Here's what I have so far (which isn't much but please bear with me):
So far I have figured out 2 sides and 1(?) angle:
S2= 42.5 (Found by subtracting the first latitude (47.5) from 90 degrees)
S3= 44.5 (Found by subtracting the second latitude (45.5) from 90 degrees)
a1=2.2 (Found by subtracting the longitudes (111.3 and 113.5) from each other)
Now, I'm trying to find the angle between Great Falls and Lemhi.
To do this, S1 would be needed, right?
To do that I used this formula: cos(S1)=cos(S2)*cos(S3)+sin(S2)*sin(S3)*cos(a1)
I plugged in my numbers a few times and couldn't seem to get a number that made sense, but eventually I came up with 44.9. Is that right? S1=44.9??
And this is where I'm not sure what to do from here. How do I find the angle between GF and Lemhi and how do I find the arc length joining the two?
(TL;DR) 1. How do I find the angle between Great Falls and Lemhi and 2. how do I find the arc length joining Great Falls and Lemhi?