An observer at the top of a tower of height 20m sees a man due East of him at an angle of depression of 27 degrees. He sees another man due

An observer at the top of a tower of height 20m sees a man due East of him at an angle of depression of 27 degrees. He sees another man due south of him at an angle of depression of 30 degrees. Find the distance between the men on the ground

$$\small{\text{
$ h=20\ m $; \quad distance $ d=\ ? $
}}
\\ \\
\small{\text{
$
d^2 =
\left(
\dfrac {h}
{ \tan{(30\ensurement{^{\circ}} ) } }
\right) ^2
+
\left(
\dfrac {h}
{ \tan{(27\ensurement{^{\circ}} ) } }
\right) ^2
$
}}
\\ \\
\small{\text{
$
d^2 = h^2
\left(
\dfrac {1}
{ \tan^2{(30\ensurement{^{\circ}} ) } }
\right)
+
\left(
\dfrac {1}
{ \tan^2{(27\ensurement{^{\circ}} ) } }
\right)
$
}}
\\ \\
\small{\text{
$
d = h
\sqrt{
\dfrac {1}
{ \tan^2{(30\ensurement{^{\circ}} ) } }
+
\dfrac {1}
{ \tan^2{(27\ensurement{^{\circ}} ) } }
}
$
}}
\\ \\
\small{\text{
$
d = 20\ m * \sqrt{ 3.69466131307 }
$
}}
\\ \\
\small{\text{
$
d= 20 * 1.92215017964 \ m
$
}}
\\ \\
\small{\text{
$
d= 38.4430035927\ m
$
}}$$