Answer :
Final answer:
To find the height of the peak, we can set up a triangle using the given angles and distances and use trigonometry to solve for the height.
Explanation:
To find the height of the peak, we can use trigonometry and set up a triangle using the given angles and distances. Let's denote the distance from the peak to the observer as 'x'.
From the first observation, we have tan(27 degrees 45 minutes) = height / (x + 1000 feet).
From the second observation, we have tan(31 degrees 30 minutes) = height / x.
Solving these two equations simultaneously, we can find the value of 'height', which is the height of the peak.
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