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

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) (Show Source): You can put this solution on YOUR website!
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

RELATED QUESTIONS
Please let me know if I'm on the right track with this. A plane is observed approaching (answered by venugopalramana)

Please let me know if I'm on the right track with this. A plane is observed... (answered by venugopalramana)

A plane is observed approaching your home at a speed of 600 miles per hour. If the angle (answered by ankor@dixie-net.com)

A plane is approaching your home, and you assume that it is traveling horizontally at... (answered by mananth)

Suppose you live 3.6 miles from a hill. From your home you see a plane directly above the (answered by Alan3354)

Suppose you live 4.4 miles from a hill. From your home you see a plane directly above the (answered by ankor@dixie-net.com)

Suppose you live about 5.1 miles from a tower. from your home you see a plane directly... (answered by ankor@dixie-net.com)

A plane passes over your head at an altitude of 5000 feet. Two seconds later you observe... (answered by ankor@dixie-net.com)

An airplane in Australia is flying at a constant altitude of 2 miles and a constant speed (answered by chessace)