Question 90236: Use the Law of Sines or Cosines:
A antenna is located at the top of a building 1000 ft. tall. From a point on the same horizontal plane as the base of the building, the angles of elevation od the top and bottom of the antenna are 65.8 degrees and 62.6 degrees, respectively. How tall is the antenna?
Answer by Nate(3500)   (Show Source):
You can put this solution on YOUR website! Prefered:
a. draw a building with an antenna on the top
b. draw a line near the base of the building to the top of the building
c. draw a line from the same spot to the top of the antenna
d. label
~ 1000 + x is the total height where x is the height of the antenna
~ b is the distance the location of the spot near the base is from the building
tan(62.6*) = 1,000/b or b = 1,000/tan(62.6*)
tan(65.8*) = (1,000 + x)/b or (1,000 + x)/tan(65.8*) = b
b = b
1,000/tan(62.6*) = (1,000 + x)/tan(65.8*)
1,000*tan(65.8*)/tan(62.6*) = 1,000 + x
1,000*tan(65.8*)/tan(62.6*) - 1,000 = x
about 143.5 feet
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