I really need a lot of help with this question. Answer step by step and well and explain every conclusion you've got.

Obs : The answer is 60°, but, i need to understand, if possible, why this is the value

I really need a lot of help with this question Answer step by step and well and explain every conclusion youve got Obs The answer is 60 but i need to understand class=

Respuesta :

Step-by-step explanation:

In a normal triangle, there is a formula as following:

+) cosine of an angle = [tex]\frac{Adjacent side 1^{2}+Adjacent side 2^{2} - Opposite side^{2}}{2*Adjacent side 1 * Adjacent side 2}[/tex]

Angel B = 30° has:

+) 2 adjacent sides: BC and AB

+) Opposite side: AC

=> We have:

cosine ∠B = [tex]\frac{BC^{2}+AB^{2}-AC^{2} }{2*AB*BC}[/tex]

=> cosine 30°  = [tex]\frac{(2\sqrt{3})^{2} + 4^{2} - AC^{2} }{ 2 *4*2\sqrt{3} }[/tex]

=> [tex]\frac{\sqrt{3} }{2} = \frac{28 - AC^{2} }{16\sqrt{3} }[/tex]

=> 2 x (28 - AC^2) = 48

=> AC^2 = 4

We have:

[tex]BC^{2} = (2\sqrt{3} )^{2} =12[/tex]

[tex]AB^{2} = (4 )^{2} =16[/tex]

[tex]AC^{2} = 4[/tex]

=> [tex]AC^{2} +BC^{2} = AB^{2}[/tex]

According the inverse Pythagorean theorem, ABC is the right angle triangle with Angle ACB = 90°

=> X + 30 = 90

=> X = 60°

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