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Please answer this question with whole method

Answer»

Good question...

SEE, ABC IS a right ANGLED triangle
apply PYTHAGORAS theorem to find the value of x.

(5 - x) {}^{2} + {x}^{2} = { (\sqrt{13}) }^{2} \\ 25 + 2 {x}^{2} - 10x = 13 \\ 2 {x}^{2} - 10x + 12 = 0 \\ {x}^{2} - 5x + 6 = 0 \\ {x}^{2} - 2x - 3x + 6 = 0 \\ x(x - 2) - 3(x - 2) = 0 \\ (x - 3)(x - 2) = 0 \\ x = 3 \: or \: 2 \: \\
if you will PUT x=3
sides will be 2,3,√13

and if you will put x=2
sides will be 2,3,√13

since sides are same... no matter what value you take

then.,
if u take x=2
\sin( \alpha ) + \sin( \beta ) \\ = \frac{2}{ \sqrt{13} } + \frac{3}{ \sqrt{13} } \\ = \frac{5}{ \sqrt{13} }


mark as brainliest if helped



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