How Tall Is That?

Scientists using remote sensing photos can estimate the height of objects in the photos by noting the time of day and studying the length and angles of shadows. Students can do the same. The clinometer or biltmore stick is available in many education stores. Students can also use two ancient but relatively accurate ways of measuring height which are described below.

Objective:
Students will find the height of object x using the ratio of the lengths of shadows of two objects.

Grade Level: 4-5

Time Duration: 1 class periods
Vocabulary: ratio, proportion, scale
Grouping: pairs

Materials Per Group:

pre-measured reference stick at least one foot long

measuring tape

paper and pencil

a field or large open space

Procedure:

measure the reference stick to the nearest inch

place stick vertically in the ground

measure the shadow of the stick

with measuring tape measure the shadow of a tree (if there is no tree, have students measure each other's shadow)

calculate the tree (or student) height (solve for x) with a ratio by cross multiplying

See the figure below:

American Indians in the northwest had a related method of measuring the height of an object. They would walk away from something for which they wanted to know the height, say a tree, until they could see the top of the tree while they bent over and held their ankles and looked between their legs.
Then, they would walk back and count each step as they returned to the tree. The number of steps they counted was height of the tree. This method assumes the object measured is vertical and each step is about a foot.
The shadow ratio technique can be used to simulate measurement of objects in remote sensing photos. Use a six inch ruler for your pre-measured stick. Use quart milk cartons and twigs to represent buildings and trees. Place your "town" on butcher paper.
(At this point, you might want your students to do the exercise called Hometown USA , since in that exercise the students construct a scale model of a town as well.) Aim a strong light at the town so your town casts a shadow. Measure your stick's shadow and the shadows of your houses and trees. Find the ratios.
To simulate how a remote sensing scientist might use this ratio method to find the height of objects in a remotely sensed image, try using a Polaroid photo of this set-up shot from overhead. Be sure you are shooting straight down on the model village. Have students measure and compute the ratios of objects as seen from above. Look for shadows in remote sensing photos.

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