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You can use indirect measurement to find the height of objects that are not easily able to measure, for example, how tall a building is or how high up a flagpole would be.

First, we need to review what a ratio is. A __ratio__ is a comparison of two numbers. And when we compare two ratios, we form a __proportion__.

Secondly, we need to assess the information that is given. In other words, how can we create a ratio and a proportion from the example?

You can use indirect measurement to compare the height of two objects and the shadow of their objects. This is called __shadow reckoning__. Be careful when setting up the proportion, because you want to make the comparison of objects that are similar.

Look at this example on how to find the height of an object using indirect measurement and shadow reckoning.

__Example.__** If A 12 foot flagpole casts a shadow of 9 feet, how tall is a building that casts a shadow of 30 feet?**

step #1 - set up a ratio that compares the height of the flagpole to the height of the building

step #2 - set up a second ratio that compares the shadows length of the flagpole to the shadows length of the building

step #3 - set the two ratios equal to each other to form a proportion. Solve by cross multiplying.

Source: glencoe course 2 textbook