Question 192748
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We'll see the man standing on the building.
{{{drawing(400,400,-2,15,-1,8,line(0,0,0,6),line(0,6,2,6),line(2,6,2,0),line(-2,0,15,0),circle(1.7,6.5,.2),line(1.7,6.4,1.7,6.2),line(1.7,6.2,1.6,6),line(1.7,6.2,1.8,6),line(1.6,6.3,1.8,6.3),green(line(2,6,14,0)),green(locate(7,3.4,shadow=100ft)),green(arrow(-.5,0,-.5,6)),green(locate(-1.8,5,220ft)),line(15,0,14,-.5),line(14,0,13,-.5),line(13,0,12,-.5),line(12,0,11,-.5),line(11,0,10,-.5),line(10,0,9,-.5),line(9,0,8,-.5),line(8,0,7,-.5),line(7,0,6,-.5),line(6,0,5,-.5),line(5,0,4,-.5),line(4,0,3,-.5),line(3,0,2,-.5),line(2,0,1,-.5),line(1,0,0,-.5),line(0,0,-1,-.5),line(-1,0,-2,-.5),green(line(2.2,6,15,6)),red(locate(3.5,5.8,sigma)),red(locate(12.7,.4,sigma)),locate(7,6.4,horizontal),red(line(3,8,13,-1)),red(line(13,8,3,-1)))}}} ---> This does not make sense, being 220ft tall building only casting 100ft shadow. 


*Remember, the shadow serves as the hypotenuse, and is equal to the sq.root of the sum of the squares of the two sides. Being the building 220 ft tall is impossible.


*In a Right Triangle, the hypotenuse is always the longest side.


If you add another "0" on the length of the shadow, making <font color=red>1000 ft</font> on a 220ft tall building,  then we can solve by Trigo function.

{{{drawing(400,400,-2,15,-1,8,line(0,0,0,6),line(0,6,2,6),line(2,6,2,0),line(-2,0,15,0),circle(1.7,6.5,.2),line(1.7,6.4,1.7,6.2),line(1.7,6.2,1.6,6),line(1.7,6.2,1.8,6),line(1.6,6.3,1.8,6.3),green(line(2,6,14,0)),red(locate(7,3.4,shadow=1000ft)),green(arrow(-.5,0,-.5,6)),green(locate(-1.8,5,220ft)),line(15,0,14,-.5),line(14,0,13,-.5),line(13,0,12,-.5),line(12,0,11,-.5),line(11,0,10,-.5),line(10,0,9,-.5),line(9,0,8,-.5),line(8,0,7,-.5),line(7,0,6,-.5),line(6,0,5,-.5),line(5,0,4,-.5),line(4,0,3,-.5),line(3,0,2,-.5),line(2,0,1,-.5),line(1,0,0,-.5),line(0,0,-1,-.5),line(-1,0,-2,-.5),green(line(2.2,6,15,6)),red(locate(3.5,5.8,sigma)),red(locate(12.7,.4,sigma)),locate(7,6.4,horizontal),red(locate(2.5,5.5,beta)),red(locate(2.3,.5,90^o)))}}}
Solving by Trigo Function:
{{{sin(sigma)=opp/hyp}}}
{{{sin(sigma)=220ft/1000ft}}}
{{{sigma=sin^(-1)(220/1000)}}}
{{{red(sigma=12.7^o=13^o)}}} ---> This is the angle between the end of the shadow and the ground.


For the Angle between the shadow and the vertical side of the building:
{{{180=90+sigma+beta}}}
{{{180=90+13^o+beta}}}
{{{beta=180-90-13}}}
{{{red(beta=77^o)}}}, Answer


Thank you,
Jojo</font>