Ratios and Rates

UK Secondary (7-11)

Too tall to measure (Investigation)

Lesson

Have you ever wondered how tall a building or large tree was, but couldn't reach up high enough to measure it? In this investigation, you'll use proportions to find the height of a large object of your choice.

Materials

- Measuring Tape
- Paper & Pencil to record your measurements
- Beautiful, sunny day (best done some time before the Sun is directly above!) - Please put sunscreen on!

- Use the measuring tape to measure your own height. Record your height.
- Use the measuring tape to measure your shadow. Record the length of your shadow.
- Pick an object that is too tall to measure, but its entire shadow is visible. If you're in class, be sure to ask your teacher before traveling off!
- Use the measuring tape to measure the object's shadow. Record the length of the shadow.
- Use the following proportion to calculate the height of the object:

Let $H_y$`H``y` be your height, $S_y$`S``y` be the length of your shadow, $H_o$`H``o` be the height of the object and $S_o$`S``o` be the length of the object's shadow.

$\frac{H_y}{S_y}=\frac{H_o}{S_o}$`H``y``S``y`=`H``o``S``o`

If you desire, you can first test this out with objects you know the height of.

Questions to Think About

1. What if you did the same thing with another person who is a different height than you are, and did it at a different time of day? Would your results still be the same?

2. Did you do any rounding with your measurements? How do you think this affected the precision and accuracy of your answer?