Concept explainers
View from a Satellite The figures on the next page indicate that the higher the orbit of a satellite, the more of the earth the satellite can “see.” Let θ, s, and h be as in the figure, and assume that the earth is a sphere of radius 3960 mi.
- (a) Express the angle θ as a function of h.
- (b) Express the distance s as a function of θ.
- (c) Express the distance s as a function of h. [Hint: Find the composition of the functions in parts (a) and (b).]
- (d) If the satellite is 100 mi above the earth, what is the distance s that it can see?
- (e) How high does the satellite have to be to see both Los Angeles and New York, 2450 mi apart?
(a)
To Express: The angle of elevation
Answer to Problem 42E
The expression that represents the angle of elevation
Explanation of Solution
Given:
The below figure show the length
Formula Used: Trigonometric Property of tangent:
Calculation:
Trigonometric Property of tangent is,
Substitute s for adjacent and
Simplify further to get the value of
Thus, the expression that represents the angle of elevation
(b)
To Find: The angle of elevation
Answer to Problem 42E
The angle of elevation of the sun when the shadow of the pole is
Explanation of Solution
Given:
The length of the shadow is
Calculation:
From part (a) we get the expression,
Substitute
Thus, the angle of elevation of the sun when the shadow of the pole is
Chapter 6 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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