Question

Corin measures the apparent height of a tower 800 feet away by holding a ruler in front

of her eye and observing that the tower appears to be 9 inches tall. The apparent height h
(in inches) varies inversely with Corin's distance d (in feet) from the tower. Write an
equation that gives d as a function of h. How tall would the apparent height of the tower
be if she was standing 2000 feet away from the tower? Show your work.

Answer 1

Since the apparent height h of the tower varies inversely with Corin's distance d from the tower, we know that h and d are inversely proportional. This means that the product of h and d is constant. We can write this relationship as:

hd = k

where k is a constant.

We can find the value of k by substituting the known values of h and d:

9 inches * 800 feet = k

Solving for k, we find that k = 7200 inches * feet.

Since h and d are inversely proportional, we can write the inverse relationship as:

d = k / h

Substituting the value of k that we found earlier, we have:

d = 7200 inches * feet / h

To find the apparent height of the tower if Corin is standing 2000 feet away, we can substitute 2000 for d in the equation above:

h = 7200 inches * feet / 2000 feet = 3.6 inches

Therefore, the apparent height of the tower would be 3.6 inches if Corin is standing 2000 feet away.

Explanation: