A metallic sphere is suspended on stationary wall with the help of a…

$From\; the\; figure\; in\; equilibrium$

$Tsin\theta =N$
$Tcos\theta =W$
⇒ tanθ = N/W​
$\Rightarrow N=Wtan\theta$

$As\; body\; is\; in\; equilibrium\; net\; force\; is\; zero$

$\Rightarrow \; \$\backslash vec\{N\}\; +\; \backslash vec\{T\}\; +\; \backslash vec\{W\}\$\; =\; 0$

Normal force N and Gravitational force W are at right angle so their resultant must balance tension force.

$\Rightarrow \; \$T^2=N^2\; +\; W^2\$$