Find the angle between great falls and lemhi

Assignment Help Mathematics
Reference no: EM131016361

The Lewis and Clark Expedition 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 Earth when computing the distance that they traveled. Assume that the radius of Earth is 3960 miles.

1. Great Falls is at approximately 47.5°N and 111.3°W. Lemhi is at approximately 45.5°N and 113.5°W. (We will assume that the rivers flow straight from Great Falls to Lemhi on the surface of Earth.) This line is called a geodesic line. Apply the Law of Cosines for a spherical triangle to find the angle between Great Falls and Lemhi. (The central angles are found by using the differences in the latitudes and longitudes of the towns. Then find the length of the arc joining the two towns. (Recall s = r)

2. From Lemhi, they went up the Bitteroot River and the Snake River to what is now Lewiston and Clarkston on the border of Idaho and Washington. Although this is not really a side to a triangle, we will make a side that goes from Lemhi to Lewiston and Clarkston. If Lewiston and Clarkston are at about 46.5°N 117.0°W, find the distance from Lemhi using the Law of Cosines for a spherical triangle and the arc length.

3. How far did that explorers travel just to get that far?

4. Draw a plane triangle connecting the three towns. If the distance from Lewiston to Great Falls is 282 miles and the angle at Great Falls is 42° and the angle at Lewiston 48.5°, find the distance from Great Falls to Lemhi and from Lemhi to Lewiston. How do these distances compare with the ones computed in parts (1) and (2)?

Reference no: EM131016361

How many different scoring scenarios are possible

How many different scoring scenarios are possible if the game is settled in the first round of 10 penalty kicks, where the round ends once it is impossible for a team to equ

Explain walkway is formed by laying squares

A square fountain that is 15 feet on each side is surrounded by a walkway that is three feet wide. if the walkway is formed by laying squares that are one yard on each side

How much does each type of part cost

a company orders 2 types of parts, brass and steel. One shipment contains 3 brass and 10 steel parts for a total cost of $48. A second shipment contains 7 brass and 4 steel

Interest and applications of derivatives

A person's fortune increases at a rate to the square of they're present wealth. If the person had one million dollars a year ago and has two million today then how much will

Determine the probability of obtaining a defective phone

Use your simulation results to determine the probability of obtaining a defective phone for each simulation if an outcome of 1 or 2 is considered to be a defective phone, sh

Possible system of equations

Consider the set of points (x, y, z) defined by the set of equations below: Find a 2 x 3 system of linear equations having this set of points as its solution set.

When will the object hit the ground

An object is thrown upward from the top of a 48 foot building, with an initial velocity of 32 feet per second. The height h of the object after t seconds is given by the qua

Evaluate the exact value of the trigonometric functions

Evaluate the exact value of the trigonometric functions - Use common trigonometric identities for the functions given to find the indicated trigonometric functions.

Reviews

Write a Review

 
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd