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Question 260073: A flagpole is mounted on top of a public library building. From a point 50 feet in front of the library, the angle of elevation TO THE BASE of the flagpole is 55º and the angle of elevation TO THE TOP of the flagpole is 62º. Find the height of the flagpole.
Answer by dabanfield(803)   (Show Source):
You can put this solution on YOUR website! A flagpole is mounted on top of a public library building. From a point 50 feet in front of the library, the angle of elevation TO THE BASE of the flagpole is 55º and the angle of elevation TO THE TOP of the flagpole is 62º. Find the height of the flagpole.
Let point A be the base of the building, B the foot of the flagpole, C the top of the flagpole and D the point 50 feet from the base.
Then AC = AB+BC is the distance to the top of the flagpole.
Since triangles ADB and ADC are both right triangles we have:
tangent 55 = AB/AD = and
tangent 62 = AC/AD = AC/AD = (AB+BC)/AD = AB/AD + BC/AD = tangent 55 + BC/50
Solve for BC:
BC = 50*(tangent 62 - tangent 55)
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