Question 1020021
<pre>
In the figure below, the aeroplane is at A.
AH = 1050 m is the horizontal distance.
T = the top of the control tower.
B = the base of the control tower.

We want to find TB, the height of the tower,
and AB, the shortest distance from the aeroplane
to the base of the tower.

{{{drawing(400,1792/5,-1,11.5,-10.2,1,
locate(0,.5,A), locate(10.5,.5,H),
locate(10.6,-7.4,T),locate(10.6,-8.9,B),
green(line(0,0,10.5,0),line(10.5,0,10.5,-7.628696544)),
line(10.5,-7.628696544,10.5,-9.127510747),
locate(5,.5,1050),
red(arc(0,0,7,-7,324,360)),locate(3.5,-.9,"36°"),

red(arc(0,0,11,-11,319,360)),locate(5.4,-1.8,"41°"),

red(line(0,0,10.5,-9.127510747), line(0,0,10.5,-7.628696544)) )}}} {{{(matrix(16,1,
HT/(AH)=tan("36°"),
HT=AH*tan("36°"),
HB/(AH)=tan("41°"),
HB=AH*tan("41°"),
TB=HB-HT,
TB=AH*tan("41°")-AH*tan("36°"),
TB=AH(tan("41°")^""-tan("41°")),
TB=1050(0.8693-0.7265),
TB=matrix(1,2,149.9,m),
"---------------",
AH/(AB)=cos("41°"),
AH=AB*cos("41°"),
AH/cos("41°")=AB,
1050/cos("41°")=AB,
1050/0.7547=AB,
AB=matrix(1,2,1391.3,m)
))}}}

Edwin</pre>