We shall use the fact that the height of the giant balloon from top to bottom is h , and its bottom is floating 20ft above the ground level.
Also, the length of the tether attached to the top the balloon is L.
A person of height 3ft holding that tether is standing 100ft ahead of the balloon.
Let, the angle of elevation from the person to the top of the balloon be theta. The figure can be drawn as shown above.
a.
From the figure in right triangle ABC, distance of the balloon from the person’s head AB=h+17
Length AB=h+17
Now, in right triangle ABC , by using the Pythagoras theorem
L^2=(h+17)^2+100^2
L^2=h^2 + 34h + 10289
L=sqrt(h^2 + 34 h + 10289)-> equation for the length
b.
In the right triangle ABC we can see that
cos(theta)=adj/hyp=100/L
=>theta=cos^-1(100/L)
c.
[ATTACH=full]1175[/ATTACH]
tan(35)=y/100
y = 100 tan(35°)
y =70.02ft
h=y-20+3
h=70.02-20+3
h=53.02ft
