contestada

Based on the diagram, which expresses all possible lengths of segment AB? AB = 25 27 < AB < 81 AB = 85 AB< 27 or AB > 81

Respuesta :

Nirina7
The answer

according to the figure, we can solve this problem only by applying sines rule:
that is 
sinA/a  = sinB/b = sinC /c

As we observe,  sin A /54  = sin B/27 = sin C/ c, and c = AB

besides, sinC > sinB > sinA  , so the only answer possible is 
27 < AB < 81 



calculista

we know that

The sum of the lengths of any two sides of a triangle is greater than the length of the third side (Triangle Inequality Theorem)

So

see the attached figure to better understand the problem

1) [tex] AC+BC > AB [/tex]

[tex] 27+54 > AB\\ 81 > AB\\ AB < 81 [/tex]

2) [tex] 27+AB > 54 [/tex]

[tex] 27+AB > 54\\ AB > 54-27\\ AB > 27 [/tex]

3) [tex] 54+AB > 27 [/tex]

[tex] 54+AB > 27\\ AB > 27-54\\ AB > -27 [/tex]

therefore

the answer is the option

[tex] 27 < AB < 81 [/tex]

Ver imagen calculista

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