choccocakee
choccocakee choccocakee
  • 26-05-2020
  • Mathematics
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If you're good at trig pls help meeeeeee

Pls show full working out and round answer to nearest kilometre

If youre good at trig pls help meeeeeee Pls show full working out and round answer to nearest kilometre class=

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Ultroid Ultroid
  • 26-05-2020

*flashbacks to honors trig in 9th grade*

...Anyway. We're given that the bearing from A to C is [tex]330^\circ,[/tex] so that means that the counterclockwise angle from the north to C is [tex]30^\circ.[/tex] Therefore, [tex]\angle BAC=50^\circ+30^\circ=80^\circ.[/tex]

Now, we apply the law of cosines:

[tex]BC^2&=AC^2+BC^2-2(AC)(BC)\cos\angle BAC[/tex]

[tex]BC^2&=65^2+135^2-2(65)(135)\cos 80^\circ=22450-17550\cos 80^\circ[/tex]

[tex]\boxed{BC\approx 139\text{ km}}.[/tex]

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