The height of a hill - Math Central

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Question from Amber, a student:

Hi, my name is Amber and I am having a problem with my trig homework.
Here is the question. Thanks for the help.

A surveying team determines the height of a hill by placing a 12-foot pole at the top
of the hill and measuring the angles of elevation to the bottom and to the top of the pole.
They find the angels of elevation. Describe how to find the height of the hill.

Hi Amber,

diagram

S is the position of the survey team and them measure the angles RSQ and RSP. Write an expression for the tangents of these angles and solve for y.

Penny

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