SOLUTION: 2 buildings are seperated by an alley. Joe is looking out of a window 60 feet above the ground in one building. He observes the measurement angle of depression of the base of the s

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Question 64906This question is from textbook ALgebra 1
: 2 buildings are seperated by an alley. Joe is looking out of a window 60 feet above the ground in one building. He observes the measurement angle of depression of the base of the second building to be 50 degrees and the angle of elevation of the top to be 40 degrees.How high is the second building? This question is from textbook ALgebra 1

Answer by venugopalramana(3286) About Me  (Show Source):
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2 buildings are seperated by an alley. Joe is looking out of a window 60 feet above the ground in one building. He observes the measurement angle of depression of the base of the second building to be 50 degrees and the angle of elevation of the top to be 40 degrees.How high is the second building?
LET BUILDING 1 BE BW WITH B AT THE BOTTOM (GROUND) AND W BE WINDOW.LET THE SECOND BUILDING BE GT,WITH G AT THE GROUND ANT T AT THE TOP.LET A HORIZONTAL LINE FROM W MEET THE SECOND BULDING LINE GT AT X.
ANGLE XWG=50 DEG.
ANGLE XWT = 40 DEG.
BW = 60 ' = GX
IN RIGHT TRIANGLE GWX
TAN(XWG)=GX/XW = 60/XW
XW = 60 COT(50)
IN RIGHT TRIANGLE WXT
TAN(TWX) = TAN(40)= TX/XW
TX = 60COT(50)TAN(40)
GT = GX+XT = 60+60COT(50)TAN(40)= 306.5'