1. A child stands before a tall building and wants to know how high it is. She notices that it is a sunny day, so armed with a meter stick, the fact that she is 1.2 meters tall, and a knowledge of similar triangles, she proceeds to measure the building’s height by comparing the length of her shadow to the length of the building’s shadow.

A. Draw a diagram that depicts the situation in the problem and label those quantities the child can directly measure herself.

In order to help the child measure the height of the building using similar triangles, let's draw a diagram to depict the situation.

First, we'll start with a vertical line to represent the building. Label this line as "Building".

Next, draw another vertical line that represents the child standing in front of the building. Label this line as "Child".

Then, draw two horizontal lines coming from the top of each vertical line, representing the shadows. Label one of these lines as "Building Shadow" and the other as "Child Shadow".

Finally, label the height of the child as "1.2 meters" on the Child line.

Now, the child can directly measure her own height using a meter stick, which is 1.2 meters. She can also directly measure the length of her own shadow and the length of the building's shadow. These measurements will be used to calculate the height of the building using similar triangles.