Math CentralQuandaries & Queries


Question from Scott:

If I have a hole three foot in circumference that runs at a 15degree angle from the surface and continues for a length of 100 feet, how deep would the hole be at 100 feet?

Hi Scott,

You are looking for d in my diagram


The tangent of an angle in a right triangle is the length of the side opposite the angle divided by the length of the hypotenuse. In your situation this is

sin(15o) = d/100

and thus

d = 100 sin(15o)

Use your calculator to find 15o (make sure it is in degree mode) and then multiply by 100.


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