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We can model this problem with two similar triangles. The small triangle is formed by the woman and her shadow. The larger one is formed by the tower and its shadow.
To solve the problem, we use the math fact that corresponding sides of similar triangles are proportional. That means that we can set up ratios to show the relationships between side lengths in the two triangles.
Let the variable t be the height of the tower. Here is one proportion we can use:
The ratio of the [height of the tower] to [the height of of the woman] is equal to the ratio of the [length of the tower’s shadow] to the [length of the woman’s shadow].
In algebra, that looks like this:
t / 5 = 42 / 12.
Now, we just need to solve for t.
Multiply both sides of the equation by 5:
t = 5 * (42 / 12)
t = 210 / 12
t = 17.5
The tower is 17.5 ft tall.