= Solution
For the <oblique coupling of parallel Hertzian dipoles>, a lossless <Hertzian dipole> has directional gain $G(\theta)=\tfrac32\sin^2\theta$. The separation is $r=\sqrt2d$, and both transmitting and receiving patterns have $\sin^2\theta=1/2$, so $G_t=G_r=3/4$. <Reciprocity> gives matched receiving effective area $A_e=\lambda^2G_r/(4\pi)$. The emitted polarization matches the transverse projection of the receiving dipole axis, so there is no additional polarization mismatch. Consequently
$$
\boxed{P_L=\frac{PG_t}{4\pi r^2}\frac{\lambda^2G_r}{4\pi}
=\frac{9P\lambda^2}{512\pi^2d^2}.}
$$
Both the off-axis transmitting pattern and the off-axis receiving aperture matter. This assumes the stated far field, conjugate matching and negligible dissipative antenna losses.
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