If angle of depression is 65°, how far is he from the base?

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yaong

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If angle of depression is 65°, how far is he from the base?

In 1906, Teddy Roosevelt designated Devils Tower National Monument in northeast Wyoming as the first national monument in the United States. The tower rises 1280 feet above the valley of the Bell Fourche.

If a person at the top of Devils Tower sees a hiker at an angle of depression of 65 degrees, how far is the hiker from the base of Devils Tower?

The answer is about 596.9 ft, but I don't know how to get the answer. Please help.
 
What are they calling the angle of depression?. I would think it's the angle formed from where the person is looking down from the tower. [1]

The answer you have posted would put the angle formed from the person on the ground looking up at the person on the tower. [2]

1280tan(65)=2744.97...[1]

1280cot(65)=596.87...[2]

stowermt8.gif
 
Re: Solving Right Triangles. SOHCAHTOA <hard>

yaong said:
In 1906, Teddy Roosevelt designated Devils Tower National Monument in northeast Wyoming as the first national monument in the United States. The tower rises 1280 feet above the valley of the Bell Fourche.
If a person at the top of Devils Tower sees a hiker at an angle of depression of 65 degrees, how far is the hiker from the base of Devils Tower?

The answer is about 596.9 ft, but I don't know how to get the answer. Please help.[/img][/code]
Click to expand...

The angle of depression (or elevation) is always measured between the line of sight from observor to object and the HORIZONTAL llne through the observation point.

Code: 
              Top
               |-----
               | \ 65 degrees
               |  \
      1280     |   \
               |    \
               |      \
               |______\ hiker
                   x

The angle at the ground, formed between the hiker's line of sight and the top of the tower, is the angle of elevation, and it is equal to the angle of depression for someone looking DOWN.

So, tan 65 = 1280 / x

x tan 65 = 1280
x = 1280 / (tan 65)

I hope this helps you.
 
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