Lesson 19

The Shadow Knows

Let’s use shadows to find the heights of an object.

19.1: Notice and Wonder: Long Shadows and Short Shadows

What do you notice? What do you wonder?

Photograph of 3 pens standing upright. Lamp on right. Longest shadow formed by pen on far left, shorter shadow on middle pen, no shadow on pen on right.
Photograph of 3 pens standing upright forming shadows on the desk

19.2: Objects and Shadows

Photograph of 2 boys, a man, and a lamp post, each have a shadow to their left.

Here are some measurements that were taken when the photo was taken. It was impossible to directly measure the height of the lamppost, so that cell is blank.

height (inches) shadow length (inches)
younger boy 43 29
man 72 48
older boy 51 34
lamppost 114
  1. What relationships do you notice between an object’s height and the length of its shadow?

  2. Make a conjecture about the height of the lamppost and explain your thinking.

19.3: Justifying the Relationship

Explain why the relationship between the height of these objects and the length of their shadows is approximately proportional.

Photograph of 2 boys, a man, and a lamp post. Triangles drawn using person or post as height and its shadows as the base.


19.4: The Height of a Tall Object

  1. Head outside. Make sure that it is a sunny day and you take a measuring device (like a tape measure or meter stick) as well as a pencil and some paper.
  2. Choose an object whose height is too large to measure directly. Your teacher may assign you an object.

  3. Use what you have learned to figure out the height of the object! Explain or show your reasoning.