contestada

In the right triangle shown, A = 30° and AC = 12.
How long is AB?
Answer exactly, using a radical if needed.

Respuesta :

[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] .

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