Giant Character Balloon

[nycmathguy]

Section 4.8

 

[MathLover1]

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.

tan(35)=y/100
y = 100 tan(35°)
y =70.02ft

h=y-20+3
h=70.02-20+3
h=53.02ft

 

[nycmathguy]

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.
View attachment 1175
tan(35)=y/100
y = 100 tan(35°)
y =70.02ft

h=y-20+3
h=70.02-20+3
h=53.02ft

Thank you so much. At least I tried, right? The important thing is to try even when the answer is wrong or like in this case, very wrong.

 

[nycmathguy]

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.
View attachment 1175
tan(35)=y/100
y = 100 tan(35°)
y =70.02ft

h=y-20+3
h=70.02-20+3
h=53.02ft

For part (a), to find AB = length, I need to know h and plug and chug. Correct?

For part (b), once I find the length AB from part (a), I would then simply plug and chug. Correct?

For part (c), you found the height to be 53.02 feet. If I wanted to find the height from the height of the balloon to ground level, I would then simply add 20 feet to 53.02 feet. Correct?

 

[nycmathguy]

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.
View attachment 1175
tan(35)=y/100
y = 100 tan(35°)
y =70.02ft

h=y-20+3
h=70.02-20+3
h=53.02ft

For part (a), to find AB = length, I need to know h and plug and chug. Correct?

For part (b), once I find the length AB from part (a), I would then simply plug and chug. Correct?

For part (c), you found the height to be 53.02 feet. If I wanted to find the height from the height of the balloon to ground level, I would then simply add 20 feet to 53.02 feet.