A helicopter on a joy flight over Kakadu National Park
travels due east for 125 km, then on a bearing of 215
for 137 km before returning to its starting point. Find the
total length of the journey, correct to the nearest kilometre.

  383.4 km

Step-by-step explanation:

The interior angle at the first turning point in the triangular flight path has measure 270° -215° = 55°. The law of cosines can be used to find the length of the final leg:

  c² = a² +b² -2ab·cos(C)

  c = √(125² +137² -2·125·137·cos(55°)) ≈ √14749.01 ≈ 121.4

The total length of the journey is then ...

  round trip = 125 +137 +121.4 = 383.4 . . . km

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In the attachment, the number at the bottom is the sum of the lengths of the two adjacent sides. The total length is then 125 +258.4 = 383.4 km.

sss (side, side, side)

sas (side, angle, side)

asa (angle, side, angle)

aas (angle, angle, side)

hl (hypotenuse, leg)

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step-by-step explanation:

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