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How Tall is the Building on the Hill?

Date: 19 Jan 1995 12:43:56 -0500
From: Anonymous
Subject: Math question

A building is 30 meters high and is on top of a hill.  The angles of 
elevation of the top and bottom of the building from a point at the foot 
of the hill are 64 degrees and 58 degrees 4 feet respectively.  How high 
is the hill?

Thanks for your help!
      Meredith Carmon

Date: 19 Jan 1995 13:26:21 -0500
From: Dr. Math Margaret Patterson
Subject: Re: Math question

Hi Meredith!!

        Thanks for writing Dr. Math.  I am not sure exactly what your
question means.  Maybe you could clarify:  What do you mean by "58 degrees
4 feet"?  Is there more to the problem?

If i ignore that part of the problem, this what we get:

    30m |                   we can draw two triangles  - one connecting the
        |                   point at the bottom to the top of the
        |                   building and one to the bottom.
         \                                      |\
          \                                     | \
     hill  \                                    |  \
            \                |\                 |   \
             \               | \          30+x  |    \
                           x |  \               |     \
                             |   \              |      \
                             |____\58           |_______\64
                                y                    y

The height of the hill is x, and the measures of the angles at the base of
the triangles are 58 and 64.  Since these are right triangles, we know that
the measures of the angles at the tops are their complements.

Then we can use the Law of Sines to form two equations and two unknowns. 
Do you know about the Law of Sines? In any triangle with sides of lenghths
A, B, and C, and the angles opposite those sides, a, b, and c.  Then

  a       b       c
----- = ----- = -----
sin A   sin B   sin C

For the first triangle, it is true that 30+x     y
				       ----- = -----
                	              sin 64   sin 26

Do the same thing for the second triangle and then solve for x.

I hope this helps.  Please write back if you have questions about this
explanation or need help further along in the problem.

-Margaret Patterson

Date: 25 Jan 1995 12:44:13 -0500
From: Anonymous
Subject: Re: Math questionn
Dear Dr. Math,

        Thanks for the help.  The answer you gave me fit the problem although 
my teacher went about a different way of getting it.  I will probably 
write again soon.  Thanks!

                           Meredith Carmon
Associated Topics:
High School Trigonometry

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