What is the bearing that the control tower should use to locate the​ aircraft?

A​ DC-9 aircraft leaves an airport from a runway whose bearing is #N42" degrees "E#. After flying for three fourths of a mile, the pilot requests permission to turn #90°# and head toward the southeast. The permission is granted. After the airplane goes #1# mile

2 Answers
EZ as pi
May 13, 2018

The bearing of the plane is #095° or S 85°E#

Explanation:

The distance of #3/4# mile after take-off, the #1# mile flown by the plane and the direct line from the control tower to the DC-9 form a right-angled triangle. It is offset from North by an angle of #42°#

Use trigonometry to find the angle at the control tower.

Opposite side = #1 # mile and adjacent side is #3/4#mile

#Tan theta = 1/(3/4) = 4/3#

#theta = 53.1°#

Taking the bearing of the runway into consideration, the bearing of the plane from North is #42°+53.1° = 095.1°#

Bearings are usually given with #3# figures, so #095°#

The other format would be in relation to the N-S line.

The place is on a bearing of #S 85° E#

Barney V.
May 13, 2018

#"bearing to locate aircraft"= 95^@7'48''#

Explanation:

#"Let the control tower be C"#

#"The aircraft turning point A"#

#"The 1 mile point B"#

#"Pythagoras:-"#

#:.a^2=b^2+c^2#

#:.a^2=(3/4)^2+(1)^2#

#:.a^2=9/16+1#

#:.sqrt(a^2)=sqrt 1.5625#

#:.a "=1.25 miles =BC"#

#"sine rule:-"#

#:.sin B/(AC)=sin A/(BC)#

#:.sin B/(0.75)=sin A/(1.25)#

#:.sin B=(0.75xx sin A)/1.25#

#:.sin B=(0.75xx1)/1.25#

#:.sin B=0.6#

#:.angle B=36^@52'12''#

#:."Bearing C-A"=42^@#

#"Bearing A-C"=42^@+180^@=222^@#

#:.angle at A=90^@#

#:."Bearing A-B"=222^@-90^@=132^@#

#:."Bearing B-A"=132^@+180^@=312^@#

#:."Bearing B-C"=312^@-36^@52'12"=275^@ 7'48''#

#:."Bearing C-B"=275^@ 7'48''-180^@=95^@ 7'48''#

#:."Bearing to locate aircraft"=95^@ 7'48''#

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