Question

помогите пожалуйста ​

Answer 1

Ответ:

$\sin^{2}(\angle A) + \cos^{2} (\angle A) = 1 \\ \sin^{2} (\angle A) = 1 - \cos^{2}(\angle A) \\ \sin(\angle A) = \sqrt{1 - \cos^{2} (\angle A) }$

$\sin(\angle A) = \sqrt{1 - {( \frac{1}{ \sqrt{10} }) }^{2} } = \sqrt{1 - \frac{1}{10} } = \sqrt{ \frac{9}{10} } = \frac{3}{ \sqrt{10} }$

$\tan(\angle A) = \frac{ \sin(\angle A) }{ \cos(\angle A) }$

$\tan(\angle A) = \frac{ \frac{3}{ \sqrt{10} } }{ \frac{1}{ \sqrt{10} } } = \frac{3}{ \sqrt{10} } \times \sqrt{10} = 3$