This post will present, set up, and figure out a solution to a real life elevation/depression problem.
Introduction: Jeff's ski resort experience and findings
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The Problems: Ascending up the gondola and observing the flag pole
Read the word problems carefully and answer the question. Show all work and steps neatly and correctly. Round answers tot he nearest tenth.
Jeff goes to Mammoth Lakes to enjoy his winter break. He it
is at an elevation of 350 feet at a camping house in a city located on a hill.
Jeff wants to see how much the ski gondola travels to take him to the top
of the biggest mountain, white smoky. When he looks up, Jeff is looking at an
angle of elevation of 13 degrees (He is looking at it while laying down on the
floor, so no eye level must be found). He knows the mountain is 995 feet tall.
From that same lodging house in the city at an elevation of 350 feet on top of a hill, he makes eye with a flag pole that is planted at sea level and is 350 feet tall. He knows that flagpole is 300 feet away. Jeff wants to know what the angle of depression is when he observes where the flag pole is planted.
The Solutions: Jeff's ski calculations
These images show the solutions to the word problems. Make sure to work out your own before taking a look.
If he knows how elevated he is and the height of the
mountain, Jeff can find the difference and set that as the value for opposite
(645 ft). We are trying to find the ski gondola's traveled distance, which is the
hypotenuse(x). We have the angle(13). We set sin13=645/x. It ends up being
2867.3 ft.
We know the adjacent distance (300) and the opposite (350)
because the top of the flag pole and Jeff, which is elevated, are eye to eye.
We don't have an angle measure. We set up tan x =350/300. To isolate x, we use arc tan and plug into the calculator. The angle is 49.4
degrees.
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