Answer
$1.3\lt1.5,$ So friend is wrong
Work Step by Step
Please see the attached image first.
We can write the ratio of the building height as,
$\frac{Height\space of\space taller\space building}{Height\space of\space shorter\space building}=\frac{H_{1}+H_{2}}{H_{1}}-(1)$
By using trigonometry, we can get
$tan52^{\circ}=\frac{H_{1}}{D}=\gt H_{1}=Dtan52^{\circ}=1.28D-(2)$
$tan21^{\circ}=\frac{H_{2}}{D}=\gt H_{2}=Dtan21^{\circ}=0.38D-(3)$
$(2),(3)=\gt(1)$
$\frac{H_{1}+H_{2}}{H_{1}}=\frac{1.28D+0.38D}{1.28D}=1.3$
Since $1.3\lt 1.5$, the friend is wrong
