Question

The Sears Tower of Chicago casts a 242-foot shadow. At the same time, a 12-foot light pole casts a 2-foot shadow. Find the height of the Sears Tower.

a) 1,452 feet
b) 1,4520 feet
c) 22 feet
d) 220 feet

Answer 1

To find the height of the Sears Tower, we solve the proportion 12/2 = Sears Tower Height / 242, which gives us the height of the Sears Tower as 1452 feet (option a).

Step-by-step explanation:

The height of the Sears Tower in Chicago can be found using a proportion based on similar triangles formed by the tower and its shadow, and the light pole and its shadow. Since a 12-foot light pole casts a 2-foot shadow, we have a ratio of height to shadow length for the light pole, which can be set equal to the ratio of height to shadow length for the Sears Tower. The proportion is as follows:

Light Pole Height / Light Pole Shadow Length = Sears Tower Height / Sears Tower Shadow Length

Substituting the known values into this proportion gives us:

12 feet / 2 feet = Sears Tower Height / 242 feet

Now, we can solve for the Sears Tower Height:

12/2 = Sears Tower Height / 242

6 = Sears Tower Height / 242

Therefore, Sears Tower Height = 6 * 242 feet

Sears Tower Height = 1452 feet

So, the correct answer to the height of the Sears Tower is 1452 feet, which is option a).