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Please HELP!!!!

Artemis seeks knowledge of the width of Orion’s Belt, which is a pattern of stars in the Orion constellation.
She has previously discovered the distances from her house to Alnitak (736 light years, l.y.) and to Mintaka (915 l.y.), which are the endpoints of Orion's Belt. She also knows the angle between these stars in the sky is 3 degrees.

What is the width of Orion’s Belt? That is, what is the distance between Alnitak and Mintaka?
Do not round during your calculations. Round your final answer to the nearest light year.

Please HELP Artemis seeks knowledge of the width of Orions Belt which is a pattern of stars in the Orion constellation She has previously discovered the distanc class=

Respuesta :

Answer: 184.08 l.y.

Step-by-step explanation:

Let the width of Orion's belt is x light year.

By cosine law,

[tex](x)^2 = (915)^2+(736)^2-2\times 915\times 736 cos3^{\circ}[/tex]

[tex](x)^2 = 837225+541696-1346880 cos3^{\circ}[/tex]

[tex](x)^2 = 837225+541696-1345034.14777[/tex]

[tex](x)^2 = 33886.8522298[/tex]

[tex]x = 184.08381849\approx 184.08[/tex]

Thus, the width of the Orion's belt is 184.08 light year.

The width of Orion's belt is 184.08 light year.

Let the width of Orion's belt is x light year.

What is the low of cosine?

[tex]x^{2} =y^{2} +z^{2}-2yz cos(\theta)[/tex]

By cosine law,

[tex]x^{2} =915^{2}+736^{2} -2(915)(736)cos(3^0)\\x^{2} =837225+541696-1346880cos(3^0)\\\x^{2} =33886.8522\\x=184.0838[/tex]

Therefore,the width of Orion's belt is 184.08 light year

To learn more about the cosine low visit:

https://brainly.com/question/4372174

Thus, the width of the Orion's belt is 184.08 light year.

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