$\"\"$

\

Consider the two platforms are $\"\"$ and $\"\"$ .

\

The base is $\"\"$ .

\

Redraw the diagram :

\

$\"\"$

\

Observe the figure :

\

Two parallel lines are cut by a transversal, then consecutive angles are supplementary.

\

Therefore, $\"\"$

\

$\"\"$ .

\

From the figure $\"\"$ .

\

The sum of the angles in any triangle is $\"\"$ .

\

The two angles are $\"\"$ and $\"\"$ .

\

The remaining angle $\"\"$ .

\

$\"\"$

\

$\"\"$

\

Therefore , $\"\"$ and $\"\"$ and $\"\"$ .

\

Law of sines : $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

And $\"\"$ , $\"\"$ and $\"\"$

\

Law of sines : $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Therefore, the distance from the base to platform 2 is $\"\"$

\

The distance from platform 1 to platform 2 is $\"\"$ .

\

$\"\"$

\

The distance from the base to platform 2 is $\"\"$ .

\

The distance from platform 1 to platform 2 is $\"\"$ .