If a central angle with its vertex at the center of the earth has a measure of 1', then the arc on the surface of the earth that is cut off by this angle (known as the great circle distance) has a measure of 1 nautical mile (see the figure below). Find the number of regular (statute) miles in 1 nautical mile to the nearest hundredth of a mile. (Use 4,000 miles for the radius of the earth.) x mi 1 nautical mile Radius of Earth: 4000 miles Cengage Learning

Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Section 3.2 Question 11
**Calculating the Distance of a Nautical Mile**

**Problem Statement:**
If a central angle with its vertex at the center of the Earth has a measure of 1', then the arc on the surface of the Earth that is cut off by this angle (known as the great circle distance) has a measure of 1 nautical mile (see the figure below).

Find the number of regular (statute) miles in 1 nautical mile to the nearest hundredth of a mile. (Use 4,000 miles for the radius of the Earth.)

**Answer:**
___ mi

**Visual Explanation:**

An illustration shows a central angle, with its vertex at the center of the Earth, measuring 1'. The arc on the surface, corresponding to this angle, represents 1 nautical mile. For visual reference, the Earth's radius is indicated as 4,000 miles.

The diagram includes:
- A circle representing the Earth, with labeled geographical landmasses.
- Two radii from the Earth's center to the surface, forming the central angle of 1'.
- An arc between these radii on the Earth's surface, representing the great circle distance of 1 nautical mile.
- Annotation: "Radius of Earth: 4000 miles"

**Image Reference:**
(C) Cengage Learning
Transcribed Image Text:**Calculating the Distance of a Nautical Mile** **Problem Statement:** If a central angle with its vertex at the center of the Earth has a measure of 1', then the arc on the surface of the Earth that is cut off by this angle (known as the great circle distance) has a measure of 1 nautical mile (see the figure below). Find the number of regular (statute) miles in 1 nautical mile to the nearest hundredth of a mile. (Use 4,000 miles for the radius of the Earth.) **Answer:** ___ mi **Visual Explanation:** An illustration shows a central angle, with its vertex at the center of the Earth, measuring 1'. The arc on the surface, corresponding to this angle, represents 1 nautical mile. For visual reference, the Earth's radius is indicated as 4,000 miles. The diagram includes: - A circle representing the Earth, with labeled geographical landmasses. - Two radii from the Earth's center to the surface, forming the central angle of 1'. - An arc between these radii on the Earth's surface, representing the great circle distance of 1 nautical mile. - Annotation: "Radius of Earth: 4000 miles" **Image Reference:** (C) Cengage Learning
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