Question 495649: A flagpole 40 ft high stands on top of the Wentworth Building. From a point P in the front of Bailey's Drugstore, the angle of elevation of the top of the pole is 54.9°, and the angles of elevation of the bottom of the pole is 47.5° Find the height of the Wentworth Building.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! A flagpole 40 ft high stands on top of the Wentworth Building. From a point P in the front of Bailey's Drugstore, the angle of elevation of the top of the pole is 54.9°, and the angles of elevation of the bottom of the pole is 47.5° Find the height of the Wentworth Building.
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Draw a right triangle with the vertical leg=40+x, x representing the difference in height between the Baily Drugstore and Wentworth Bldg, and a horizontal leg=y representing the distance betweeen the two bldgs. You now have two right triangles to work with:
tan 54.9º=(40+x)/y
tan 47.5º=x/y
Height of Wentworth Bldg=40+x
..
tan 47.5=x/y
y=x/tan 47.5º
sub y in first equation
tan 54.9º=(40+x)/(x/tan 47.5º
(40+x)/x=tan 54.9º/tan 47.5)=1.3038
40+x=1.3038x
1.3038x-x=40
.3038x=40
x=40/.3038=131 ft
40+x=131+40=171 ft
Ans:
Height of Wentworth Bldg=171 ft
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