find the value of x in the triangle shown below

Answer:
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