Karina travels 5 miles at a bearing of 30° east of north to get to the supermarket. She then travels 10 miles 15° south of east to go to Anissa’s house. How far away and in what direction is Karina’s house from Anissa’s house? Draw a diagram and show your work to justify your answer. Round the distance to the nearest hundredth and the direction to the nearest degree.

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s251713 s251713 · Answer 1 · 2021-07-16T07:37:54+02:00

Answer: Karina's house is 12.28 miles away and 8 degrees south west

Step-by-step explanation: I know that this should be the answer because of edg.

EDIT: I found a blurry version of the diagram online, its attached down below.

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Omm2 Omm2 · Answer 2 · 2021-12-28T13:41:24+01:00

The distance between Karina’s house and Anissa’s house is 12.28 miles.

The diagram of the given traveling is,

We have the triangle,

By Cosine rule we have,

[tex]a^{2} =5^{2} +10^{2} -2(5)(10)cos105\\a^{2} =150.8819\\a=12.28 miles[/tex]

Then also,

[tex]cosx=\frac{5^2+150.8819-100}{2\times5\times12.283} \\=0.6178\\x=51.844[/tex]

Then

[tex]\angleEOB=90-(30+51.89)\\=8.16^{\circ}[/tex]

We can draw the diagram as follows,

Therefore, Kiran's hose is at 12.28 miles distance [tex]8^{\circ}[/tex] south of the west from Anissa's house.

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