Respuesta :

Answer:

46.4°

Step-by-step explanation:

Apply sine formula:

[tex] \frac{sin \: a}{a} = \frac{sin \: b}{b} = \frac{sin \: c}{c} [/tex]

[tex] \frac{sin \: a}{a} = \frac{sin \: c}{c} [/tex]

Plug the values

[tex] \frac{sin \: (88)}{6.9} = \frac{sin \: x}{5} [/tex]

Apply cross product property

[tex]5 \: sin \: (88) = 6.9 \: (sin \: x)[/tex]

[tex] \frac{5 \: sin \: (88)}{6.9} = sin \: x[/tex]

[tex]x = {sin}^{ - 1} ( \frac{5 \: sin \:( 88)}{6.9} )[/tex]

[tex]x = 46.4[/tex]

Hope this helps .....

Best regards!!!

Answer:

x = 46.37 degrees

Step-by-step explanation:

Using cosine rule

[tex]c^2 = a^2+b^2-2abCosC[/tex]

Where a = 5 , b = 6.9 , c = 5 and C = x (Unknown)

In the cosine rule, a and b are the sides containing the angle and c is the opposite side of the angle C

Plugging in the values:

[tex]5^2 = 5^2+6.9^2-2(5)(6.9)Cos x[/tex]

=> [tex]25 = 25 + 47.62-2(34.5)Cosx[/tex]

=> [tex]25 = 72.61 - 69 Cos x[/tex]

Subtracting 72.61 to both sides

=> [tex]25-72.61 = -69Cos x[/tex]

=> -47.61 = -69 Cos x

=> 47.61 = 69 Cos x

Dividing both sides by 69

=> Cos x = 0.69

Multiplying both sides by [tex]Cos^{-1}[/tex]

=> x = [tex]Cos^{-1}0. 69[/tex]

=> x = 46.37 degrees

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