Question

please answer fast and show steps

Answer 1

45 degree...........

Answer 2

$\sin( \alpha ) = \frac{1}{ \sqrt{5} } \: \: then \\ \cos( \alpha ) = \sqrt{1 - { \sin}^{2} \alpha } = \frac{2}{ \sqrt{5} } \\ \sin( \beta ) = \frac{1}{ \sqrt{10} } \: \: then \\ \cos( \beta ) = \frac{3}{ \sqrt{10} } \\ \sin( \alpha + \beta ) = \sin( \alpha ) \cos( \beta ) + \cos( \alpha ) \sin( \beta ) \\ \frac{1}{ \sqrt{5} } \times \frac{3}{ \sqrt{10} } + \frac{2}{ \sqrt{5} } \times \frac{1}{ \sqrt{10} } \\ \frac{5}{ \sqrt{5} \times \sqrt{10} } = \frac{ \sqrt{5} }{ \sqrt{10} } = \frac{1}{ \sqrt{2} } \\ therefore \: \: \alpha + \beta = 45 \: degree$