Miguel is 5ft 10 inches tall on a sunny day he casts a shadow of 4ft 2 inches long. at the same time, a nearby electric tower casts a shadow 8ft 9 inches long. how tall is the tower?

Given:
Miguel's height:
Actual = 5 feet 10 inches
Shadow = 4 feet 2 inches

Tower's height
Actual = x
Shadow = 8 feet 9 inches

First, we need to convert the height into inches to avoid confusion.
1 foot = 12 inches.
Miguel:
5 ft x 12in/ft = 60 inches + 10 inches = 70 inches ACTUAL
4 ft x 12in/ft = 48 inches + 2 inches = 50 inches SHADOW

Tower:
8 ft x 12in/ft = 96 inches + 9 inches = 105 inches SHADOW

Ratio of Actual to shadow:
Miguel: 70 : 50
Tower: x : 105

70 : 50 = x : 105
70*105 = 50x
7350 = 50x
7350 / 50 = x
147 = x

Actual height of the tower is 147 inches or 12 feet 3 inches long.

To check:
Miguel : 70 / 50 = 1.40
Tower : 147 / 105 = 1.40

If you would like to know how tall is the tower, you can calculate this using the following steps:

Miguel 5ft 10 inches = 70 inches tall ... 4ft 2 inches = 50 inches long shadow
tower x ft y inches = w inches high = ? ... 8ft 9 inches = 105 inches long shadow

70 * 105 = 50 * w    /50
w = 70 * 105 / 50
w = 147 inches high = 12ft 3 inches

The correct result would be 12ft 3 inches.

That they are numbers and related to each other.