Answer: 63 ft
Step-by-step explanation:
We can think of the shadow and height of objects as the catheti of a triangle rectangle.
We also know the relationship:
Tan(θ) = (opposite cathetus)/(adjacent cathetus)
if we define:
Tan(θ) = k (a real number, such that will be the same number for every object, because it depends on the angle θ that will depend on the position of the sun)
opposite cathetis = heigt.
adjacent cathetus = length of the shadow.
Then we have:
k = height/length of the shadow.
For the mailbox, we know that the height is (4 + 1/2) ft and the shadow is 6ft long, then we have the equation:
k = (4 + 1/2)ft/6ft = 0.75
Then for the ferris wheel we know:
shadow length = 84ft
we can write the same equation as above:
k = 0.75 = height/84ft
0.75*84ft = height = 63ft
The ferris wheel is 63 ft high.
