Question 1206616
<pre>

{{{drawing(400*.6,500*.6,-.5,5.5,-.5,7,

line(0,0,4.922497045,6.53237421),

line(2.8,0,4.922497045,6.53237421),
line(0,0,4.922497045,0),
green(line(4.922497045,6.53237421,4.922497045,0)),
locate(.4,.66,53^o),locate(3,.66,72^o),
locate(1.4,0,2.8),
locate(4.923,6.9,P),
locate(0,0,A), locate(2.8,0,B),
locate(3.8,0,x),
locate(5.1,3.2,h)

)}}}

{{{system(tan(53^o)=h/(2.8+x), tan(72^o)=h/x)}}}



{{{system((2.8+x)tan(53^o)=h, x*tan(72^o)=h)}}}

{{{(2.8+x)tan(53^o)= x*tan(72^o))}}}

{{{2.8tan(53^o)+x*tan(53^o)= x*tan(72^o))}}}

{{{2.8tan(53^o)=x*tan(72^o)-x*tan(53^o))}}}

{{{2.8tan(53^o)=x(tan(72^o)-tan(53^o)^""))}}}

{{{(2.8tan(53^o))/(tan(72^o)-tan(53^o))=x)}}}

{{{2.122497045=x)}}}

Substitute in

{{{x*tan(72^o)=h}}}

{{{2.122497045*tan(72^o)=h}}}

{{{6.532374213=h}}}  <--altitude of plane [answer to (b)]

{{{x/(PB)=cos(72^o)}}}

{{{x=PB*cos(72^o)}}}

{{{x/cos(72^o)=PB}}}

{{{2.122497045/cos(72^o)=PB}}}

{{{6.86854472=PB}}} <--distance between the plane and point B [answer to (a)]

Find (c) all by yourself, and round off as you were told.

Edwin</pre>