Question 1019421: You are hiking up a mountain peak. You begin hiking at a trailhead whose elevation is about 7500 feet. The trail ends near the summit whose elevation is about 2.5 miles. The horizontal distance between these two points is about 18200 feet. Estimate the angle of elevation from the trailhead to the summit. Round your answer to the nearest tenth of a degree.
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! 1) Convert 2.5 miles to feet (1 mile = 5280 feet)
2) From that total, subtract 7,500. The difference is the vertical distance you are hiking. Let's call this "a".
3) The problem says the horizontal distance is 18200. Per SOHCAHTOA, since you have the Opposite and Adjacent:
Tan(x) = Opposite/Adjacent= quotient (the quotient is the result of a division)
Next (trust me for the moment) we can re-arrange that into this:
x = tan^-1*quotient
Follow these instructions and you will learn how to do this, use your calculator.
NOTE: depending on your brand of calculator, to get the tan^-1: either '2ndF tan' or 'shift tan'. Or you may have to use one of the many online calculators.
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