Madison, South Dakota, and Dallas, Texas, are 1200 km apart and lie on the same north-south line

Name: Problem 91, Chapter 6: Precalculus Student Solutions Manual 5th
Uploaded: 2020-08-02T23:17:18-08:00
Duration: 1 min 37 s
Channel: Amy Jiang
Description: Madison, South Dakota, and Dallas, Texas, are 1200 km apart and lie on the same north-south line. The latitude of Dallas is 33^∘ N. What is the latitude of Madison?

step 1 Okay, so this time we're given that the distance between, or the link from South Dakota to Texas

Question

Madison, South Dakota, and Dallas, Texas, are $1200 \mathrm{km}$ apart and lie on the same north-south line. The latitude of Dallas is $33^{\circ} \mathrm{N}$. What is the latitude of Madison?

   Madison, South Dakota, and Dallas, Texas, are $1200 \mathrm{km}$ apart and lie on the same north-south line. The latitude of Dallas is $33^{\circ} \mathrm{N}$. What is the latitude of Madison?

Precalculus Student Solutions Manual 5th

Margaret L. Lial,… 5th Edition

Chapter 6, Problem 91

Instant Answer

Solved by Expert Amy Jiang

08/02/2020

Step 1

This is our s value. We also know that the radius of the Earth (r) is approximately 6400 km. Show more…

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Madison, South Dakota, and Dallas, Texas, are $1200 \mathrm{km}$ apart and lie on the same north-south line. The latitude of Dallas is $33^{\circ} \mathrm{N}$. What is the latitude of Madison?

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Key Concepts

Arc Length and Angular Measurement

The relationship between the distance along a circular arc (such as a meridian on a sphere) and the corresponding central angle is given by the formula s = r?, where s is the arc length, r is the radius of the circle (or sphere), and ? is the angle in radians. This concept allows one to convert a physical distance along the Earth's surface into a difference in latitude.

Latitude

Latitude is a geographic coordinate that specifies the north-south position of a point on the Earth's surface. It is measured in degrees, with 0° at the equator and up to 90° at the poles, and is used to determine how far north or south a location is.

Meridians

Meridians are imaginary lines that run from the North Pole to the South Pole, representing lines of constant longitude. When two places lie on the same meridian, their difference in position is solely in their latitude, simplifying calculations of their north-south separation.

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