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sergejj [24]
3 years ago
9

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

; 81

Mathematics
2 answers:
Thepotemich [5.8K]3 years ago
7 0
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 
<span>27 < AB < 81</span> 



Amiraneli [1.4K]3 years ago
3 0

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) AC+BC > AB

27+54 > AB\\ 81 > AB\\ AB < 81

2) 27+AB > 54

27+AB > 54\\ AB > 54-27\\ AB > 27

3) 54+AB > 27

54+AB > 27\\ AB > 27-54\\ AB > -27

therefore

the answer is the option

27 < AB < 81

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