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

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)   (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)   (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".

**********************************************************

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

**********************************************************

Answer by math_tutor2020(3817)   (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.

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