Question

Can anyone help me with this problem?

Answer 1

`\tan\Theta=(|BC|)/(|CA|)`

Use Pythagorean theorem:

`|AB|^2=|BC|^2+|CA|^2\\\\9^2=6^2+|CA|^2\\\\81=36+|CA|^2\ \ \ \ |-36\\\\|CA|^2=45\to|CA|=√(45)\\\\|CA|=√(9\cdot5)\\\\|CA|=\sqrt9\cdot\sqrt5\\\\|CA|=3\sqrt5`

`\tan\Theta=(6)/(3\sqrt5)=(2)/(\sqrt5)\cdot(\sqrt5)/(\sqrt5)=(2\sqrt5)/(5)`