A steady current I goes through a wire loop PQR having shape of a right angle triangle with $PQ=3x,PR=4xandQR=5x.$ If the magnitude of the magnetic field at P due to this loop is  $k\left(\frac{{\mu }_{0}I}{48\pi x}\right)$, find the value of k.

Below figure shows the situation described in question
 
Here  $d=4x\cos 37°=4x\times \frac{3}{5}$
Magnitude of magnetic field at  p is given as
$$\begin{gathered} B_p=\frac{{\mu }_{0}I}{4\pi d}[\sin 37°+\sin 53°] \Rightarrow B_p=\frac{{\mu }_{0}I}{4\pi \frac{12x}{5}}\left[\frac{7}{5}\right]=\frac{7}{48}\frac{{\mu }_{0}I}{\pi x} \\ \Rightarrow B_p=7\left(\frac{{\mu }_{0}I}{48\pi x}\right)\Rightarrow K=7 \end{gathered}$$