Question

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

Answer 1

$AB =6\sqrt{3}$

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:

$Hypotenuse = 12\\\alpha = 30$

$Base = AB$

Now ,

$cos\alpha = \frac{Base}{Hypotenuse}$

⇒  $cos30 = \frac{AB}{12}$

⇒  $cos30(12) = AB$

⇒  $AB =cos30(12)$

⇒  $AB =(\frac{\sqrt{3}}{2})(12)$

⇒  $AB =6\sqrt{3}$

Therefore, $AB =6\sqrt{3}$ .