Great Falls is at approximately 47.5 degrees N, and 111.3 degrees W. Lemhi is approximately 45.5...

 

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Great Falls is at approximately 47.5 degrees N, and 111.3 degrees W. Lemhi is approximately 45.5 degrees N, and 113.5 degrees W. (We will assume the rivers flow straight from Great Falls to Lemhi on the surface of Earth). Apply the Law of Cosines for Sides of a spherical triangle to find the angle between Great Falls and Lemhi. (To find b and c, subtract the latitude from 90 degrees. For example b=90-47.5. To find A, subtract the longitudes). In spherical coordinates, the arc found is an angle. To find the length of the arc joining Great Falls and Lemhi. use S-ra, where a is in radians. Assume the radius of Earth is 3960 miles. Show your work below. QUESTION 2 If Lewiston is about 46.5 degrees N, 117.0 degrees W, find the distance from Lemhi to Lewiston using the Law of Cosines for a spherical triangle and the arc length. Show your work below. QUESTION 3 Based on your results so far, what is the total distance traveled by Lewis and Clark to get from Great Falls to Lewiston? QUESTION 4 Draw a plane triangle connecting the three towns. The distance from Lewiston to Great Falls is approximately 246 miles and the angle at Great Falls is 46.4 degrees, and the angle at Lewiston is 44.1 degrees. Using plane trigonometry, find the distance from Great Falls toLemhiand fromLemhitoLewiston. Show your work below. QUESTION 5 a. Compare the total distance (Great Falls to Lemhi, and Lemhi to Lewiston) found using Spherical trigonometry with the total distance found using plane trigonometry. Why is there a difference? b. Go to the Great Circle Distance Between Two Points and enter the longitude and latitude of the cities for each part of the trip. What is the actual distance traveled? How does this compare with your spherical calculation? Use a percent error to compare. Great Falls is at approximately 47.5 degrees N, and 111.3 degrees W. Lemhi is approximately 45.5 degrees N, and 113.5 degrees W. (We will assume the rivers flow straight from Great Falls to Lemhi on the surface of Earth). Apply the Law of Cosines for Sides of a spherical triangle to find the angle between Great Falls and Lemhi. (To find b and c, subtract the latitude from 90 degrees. For example b=90-47.5. To find A, subtract the longitudes). In spherical coordinates, the arc found is an angle. To find the length of the arc joining Great Falls and Lemhi. use S-ra, where a is in radians. Assume the radius of Earth is 3960 miles. Show your work below. QUESTION 2 If Lewiston is about 46.5 degrees N, 117.0 degrees W, find the distance from Lemhi to Lewiston using the Law of Cosines for a spherical triangle and the arc length. Show your work below. QUESTION 3 Based on your results so far, what is the total distance traveled by Lewis and Clark to get from Great Falls to Lewiston? QUESTION 4 Draw a plane triangle connecting the three towns. The distance from Lewiston to Great Falls is approximately 246 miles and the angle at Great Falls is 46.4 degrees, and the angle at Lewiston is 44.1 degrees. Using plane trigonometry, find the distance from Great Falls toLemhiand fromLemhitoLewiston. Show your work below. QUESTION 5 a. Compare the total distance (Great Falls to Lemhi, and Lemhi to Lewiston) found using Spherical trigonometry with the total distance found using plane trigonometry. Why is there a difference? b. Go to the Great Circle Distance Between Two Points and enter the longitude and latitude of the cities for each part of the trip. What is the actual distance traveled? How does this compare with your spherical calculation? Use a percent error to compare.

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To answer your questions lets go through each one step by step Question 1 We have the coordinates for Great Falls 475N 1113W and Lemhi 455N 1135W We c... View the full answer