SOLUTION: A plane is observed approaching your home and you assume that its speed is 550 miles per hour. The angle of elevation of the plane is 16 degrees at one time and 57 degrees one minu

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Question 28811: A plane is observed approaching your home and you assume that its speed is 550 miles per hour. The angle of elevation of the plane is 16 degrees at one time and 57 degrees one minute later. Approximate the altitude of the plane. Round to the nearest 2 decimal places.
Answer by venugopalramana(3286) About Me  (Show Source):
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A plane is observed approaching your home and you assume that its speed is 550 miles per hour. The angle of elevation of the plane is 16 degrees at one time and 57 degrees one minute later. Approximate the altitude of the plane. Round to the nearest 2 decimal places.
LET A BE THE HOUSE,B BE THE INITIAL AND C BE THE LATER POSITION OF PLANE AFTER
1 MINUTE.CONSIDER BP AND CQ PERPENDICULARS TO THE GROUND.SO
IN RIGHT ANGLE TRIANGLE APB
ANGLE APB = 90
BP=H
ANGLE BAP = 16
SO…AP=H*COT 16

IN RIGHT ANGLE TRIANGLE AQC
ANGLE AQC = 90
CQ=H
ANGLE CAQ = 57
SO…AQ=H*COT 57
SPEED OF PLANE IS 550 MPH.HENCE IT GOES 550/60=55/6 MILES IN 1 MINUTE
SO…BC=55/6=QP=AP-AQ=H*(COT 16 - COT 57)
H= 55/(6*(COT 16 - COT 57 )
H = 3.23 MILES