Question

What is the length of AB¯¯¯¯¯?

Answer 1

If BC is your shortest like, that would make it line A of the pythagorean theorem. AC is line B, and that would make line AB the hypotenuse, or line C.
So....
a^2+b^2=c^2 
12^2+18^2=c^2
12*12=144
18*18=324
324+144=c^2
468=c^2
Because it is squared, you can divide by 2 and get your answer to line AB. 

Answer 2

Answer: The length of AB is 19.636 cm (approx).

Step-by-step explanation:

Here, ABC is a triangle,

In which AC = 18 cm, BC = 12 cm and ∠C = 79°,

By the cosine law,

$AB^2=AC^2+BC^2-2(AB)(BC) cosC$

$\implies AB^2 = 18^2 + 12^2 - 2\times 18\times 12 cos 79^{\circ}$

$\implies AB^2 = 324 + 144 - 82.4294860027$

$\implies AB^2 = 385.570513997$

$\implies AB = 19.6359495313\approx 19.636\text{ cm}$

Thus, the length of AB is 19.636 cm (approx).