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Juli2301 [7.4K]
4 years ago
15

Can anyone help me with this problem?

Mathematics
1 answer:
Leviafan [203]4 years ago
7 0
\tan\Theta=\dfrac{|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|=\sqrt{45}\\\\|CA|=\sqrt{9\cdot5}\\\\|CA|=\sqrt9\cdot\sqrt5\\\\|CA|=3\sqrt5
\tan\Theta=\dfrac{6}{3\sqrt5}=\dfrac{2}{\sqrt5}\cdot\dfrac{\sqrt5}{\sqrt5}=\dfrac{2\sqrt5}{5}

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