SOLUTION: Solve the following practical application. Provide a systematic solution with illustrations A building 20 meters high stands on the top of a hill. Form a point at the foot of

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Question 1194937: Solve the following practical application. Provide a systematic solution with
illustrations
A building 20 meters high stands on the top of a hill. Form a point at the foot of the hill,
the angles of elevation to the top and bottom of the building are 41° 27′ and 37°22′,
respectively. Find the height of the hill?
Found 3 solutions by josgarithmetic, ikleyn, math_tutor2020:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Not clear: Is the building 20 meters tall, or does its bottom sit 20 meters high, or does its top sit 20 meters high?

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

For me, every such foreword 

    "Solve the following practical application. Provide a systematic solution with illustrations"

is a clear sign and a warning   do  not  touch  "the problem".


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            Why ? - - - Because I am firmly convinced
                that making illustrations for a student
                        is not a teacher's job.

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Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Hint:
This is what the diagram could look like

The diagram was made with GeoGebra.

Points:
  • A = top of the building
  • B = base of the building
  • C = location of the observer
  • D = point needed to help form a right triangle
Further useful information:
  • The red segment (AB) is 20 meters in height
  • Angle BCD = 37°22′ = 37+22/60 = 37.36667° (approximate)
  • Angle ACD = 41°27′ = 41+27/60 = 41.45° (exact)
  • Segment BD is the height of the hill.
  • Angle BCD is marked in blue.
  • Angle ACD is marked in purple.
  • The dashed line (segment BC) is the hill itself.
Yet another hint: Break the figure into two separate right triangles ADC and BDC.
Use trigonometry to determine x and y.