Concept explainers
Mounting Climbing Several mountain climbers are located in a mountain pass between two peaks. The angles of elevation to the two peaks are
(a) Find the angle between the two lines.
(b) Approximate the amount of vertical climb that is necessary to reach the summit of each peak.
(a)
To find:
The angle between the two lines.
Answer to Problem 1PS
Solution:
The angle between the two lines is
Explanation of Solution
Given:
The angle of elevation to the two peaks are
The given diagram is shown in figure
Figure
Approach:
The sum of the angle of elevations of the two peaks and the angle between the sight to the peaks is equal to
Calculation:
Suppose the angle between two lines of sight to the peaks be
So the total of the all angles must be equal to
Therefore, the angle between the two lines is
(b)
To find:
The Approximate amount of vertical climb that is necessary to reach the summit of each peak.
Answer to Problem 1PS
Solution:
The Approximate amount of vertical climb to the peak is
Explanation of Solution
Approach:
The formula of
Here,
And the value of
Calculation:
Suppose the vertical climb for the first peak is
Consider, the vertical climb for the second peak be
Therefore, the approximate amount of vertical climb to the peak is
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Precalculus (MindTap Course List)
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