[tex]AB =6\sqrt{3}[/tex]
Step-by-step explanation:
Here we have , A = 30° and AC = 12 in a right triangle ABC . We need to find How long is AB . Let's find out:
We have following dimensions:
[tex]Hypotenuse = 12\\\alpha = 30[/tex]
[tex]Base = AB[/tex]
Now ,
[tex]cos\alpha = \frac{Base}{Hypotenuse}[/tex]
⇒ [tex]cos30 = \frac{AB}{12}[/tex]
⇒ [tex]cos30(12) = AB[/tex]
⇒ [tex]AB =cos30(12)[/tex]
⇒ [tex]AB =(\frac{\sqrt{3}}{2})(12)[/tex]
⇒ [tex]AB =6\sqrt{3}[/tex]
Therefore, [tex]AB =6\sqrt{3}[/tex] .