Concept explainers
Distance to the Moon To find the distance to the sun as in Exercise 67, we needed to know the distance to the moon. Here is a way to estimate that distance: When the moon is seen at its zenith at a point A on the earth, it is observed to be at the horizon from point B (see the following figure). Points A and B are 6155 mi apart, and the radius of the earth is 3960 mi.
- (a) Find the angle θ in degrees.
- (b) Estimate the distance from point A to the moon.
(a)
To find: The angle
Answer to Problem 62E
The angle
Explanation of Solution
Given:
Given triangle when the moon is seen at its zenith at a point
Figure (1)
Sides of the triangle, Distance between point
Calculation:
Use arc of length property for earth when moon is zenith at point
Substitute length of arc (s) is
Use radian property to change the angle into degrees,
Thus, the angle
(b)
To find: The distance from point
Answer to Problem 62E
The distance from point
Explanation of Solution
Given:
Given triangle when the moon is seen at its zenith at a point
Figure (1)
Sides of the triangle, angle between moon centre of earth to the horizon point
Calculation:
Use cosine property when moon is seen at its zenith at a point
Substitute radius of earth (adjacent) is
Further simplifying the above equation,
Thus, the distance from point
Chapter 6 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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