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B. Use the Law of Cosines 1. Calculate the length of side c. С 120° a = 7 b = 6 C С VALUATION​

B Use The Law Of Cosines 1 Calculate The Length Of Side C С 120 A 7 B 6 C С VALUATION class=

Sagot :

KANTOINEDOIXIN

LAW OF COSINES

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[tex] \large \bold{\blue{Problem:}} [/tex] Calculate the length of side c. С=120° a=7 b=6

[tex] \large \bold{\blue{Solution:}} [/tex] The oblique triangle has the given of two sides and an included angle (SAS). Find side c using the law of cosines.

  • [tex] \sf c² = a² + b² - 2ab(cos \ C) [/tex]

  • [tex] \sf c² = 7² + 6² - 2(7)(6)(cos \ 120°) [/tex]

  • [tex] \sf c² = 49 + 36 - (-42) [/tex]

  • [tex] \sf c² = 49 + 36 + 42 [/tex]

  • [tex] \sf c² = 127 [/tex]

  • [tex] \sf \sqrt{c^2} = \sqrt{127} [/tex]

  • [tex] \sf c = 11.27 [/tex]

[tex] \large \therefore \underline{\boxed{\tt \purple{c = 11.27 \: units}}} [/tex]

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MATHQUEEN456IN

[tex]\huge\underline { \mathcal{Answer}}{:}[/tex]

[tex]c = 10[/tex]

ᴀs sʜᴏᴡɴ ɪɴ ᴛʜᴇ ғɪɢᴜʀᴇ . a = 7, b = 4, C = 120°

sᴏ

[tex] {c}^{2} = {a}^{2} + {b}^{2} - 2abcos[/tex]

C

[tex] = 49 + 16 - 56 \times ( - \frac{1}{2} )[/tex]

[tex] = 93[/tex]

sᴏ

[tex]c = \sqrt{93} = 10[/tex]

(ɴᴏᴛᴇ : ᴏᴡɴ ᴀɴsᴡᴇʀ )

[tex]\huge\orange{\boxed{{ᴍᴀᴛʜǫᴜᴇ̈ᴇ̈ɴ}}}[/tex]

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