Respuesta :

Answer:

14

Step-by-step explanation:

Using the law of cosines on ΔRST, then

s² = 9² + 8² - (2 × 9 × 8 × cos111° )

   = 81 + 64 - ( 144 × cos111° )

   = 145 - (- 51.6)

   = 145 + 51 . 6 = 196.6 ( take the square root of both sides )

s = [tex]\sqrt{196.6}[/tex] ≈ 14

mixter17

Hello!

The answer is: 14

Why?

Using the law of cosines and the given information, we can find the value of s.

Law of cosines is:

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

Where,

[tex]a=s\\b=9\\c=8\\A=111(degrees)[/tex]

By substituting we have:

[tex]s=\sqrt{9^{2}+8^{2}-2*9*8*cos(111)}\\\\s=\sqrt{81+64-(144)*(-0.35)}=\sqrt{145+50.4}=\sqrt{195.4}=13.98=14[/tex]

So, the correct answer is:

[tex]s=14[/tex]

Have a nice day!

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