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Which equation correctly uses the law of cosines to
solve for the length s?
92 = 52 + 102 - 2(s)(10) cos(100°)
9 = s + 10 - 2(s)(10)cos(100)
102 = 52 + 100 – 2(s)(10)cos(100)
S2 = 92 + 102 - 2(9)(10)cos(100)

Which equation correctly uses the law of cosines to solve for the length s 92 52 102 2s10 cos100 9 s 10 2s10cos100 102 52 100 2s10cos100 S2 92 102 2910cos100 class=

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Answer:

fourth option

Step-by-step explanation:

Using the Law of Cosines in Δ STU to find s

s² = t² + u² - 2us cosS

where t = 9, u = 10 and S = 100° , thus

s² = 9² + 10² - 2(9)(10)cos100°

varshamittal029

The required law of cosines is [tex]s^{2}=9^{2} +10^{2}-2(9)(10)Cos(100)[/tex]

What is the law of cosines ?

The relation between lengths of sides of the triangle and cosines of the angles of the triangle is called law of cosines.

This law is used for SAS triangles.

The formula of law of cosines is [tex]a^{2}= b^{2}+ c^{2}-2(b)(c)Cos(A)[/tex]

Where a, b, c are sides of the triangle and A is the opposite angle of side a.

What is the length of s ?

Here in the given diagram,

SU = 9 unit, ST = 10 unit & UT = s

Also given that, ∠S = 100°

Using the law of cosines,

[tex]UT^{2} =SU^{2}+ ST^{2}-2(SU)(ST)Cos(S)[/tex]

⇒ [tex]s^{2}=9^{2} +10^{2}-2(9)(10)Cos(100)[/tex]

4th option is correct.

Learn more about Law of cosines here :

https://brainly.com/question/8288607

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