Wednesday
Wednesday: Boathouse Lab, the Shadow Stick
A grown-up holds the stick upright on the dock while Comet reads the tape. "1.73 meters tall. Close to √3."
"Shadow is 3 meters," Wren says, reading along the boards. "Height over shadow is about 0.58."
"That is √3/3," Comet says. "Tan 30°. The light is 30° above the dock. What do you notice?"
They wait, then measure again. The shadow has shrunk to match the stick. "Tan 1. Forty-five degrees."
Nova projects the three triangles side by side. "Would you like a hint? The shadow is the adjacent side every time."
A third reading: shadow 1 meter. "Height over shadow is 1.73, which is √3," Wren says. "Sixty degrees."
"Three readings, three special angles," Comet says. "Nova, log them all."
What you need
- A straight stick, broom handle or meter stick, a tape measure, chalk, and your Boathouse Log.
- A flat, open spot where the stick's shadow falls on the ground. A grown-up to hold the stick upright.
- Three different times in one afternoon, or a lamp on a table for an indoor version.
Never look at the Sun or straight into a lamp. Read the shadow on the ground, not the light.
The stick stays on the ground or in a grown-up's hands. Nothing is climbed and no ladder is used.
Chalk only on the ground. Nothing heavy is lifted alone.
Run the lab
- Measure the stick's height and write it at the top of your table.
- Hold the stick straight up. Chalk the tip of its shadow and measure the shadow's length.
- Divide height by shadow. That is the tangent of the light's angle above the ground.
- Compare the ratio with the table: √3/3 ≈ 0.58, 1, and √3 ≈ 1.73. Pick the nearest special angle.
- Repeat twice more as the light moves, or move the lamp. Record every reading.
- Draw each reading as a right triangle: stick up, shadow along, light line as the hypotenuse.
The crew's readings
The crew's numbers are made up for the Boathouse. Yours depend on your stick and your light, and that is the point of a lab.
| Shadow (m) | Stick (m) | Stick ÷ shadow | Nearest tangent | Angle |
|---|---|---|---|---|
| 3 | 1.73 | 0.58 | 0.58 | 30° |
| 1.73 | 1.73 | 1 | 1 | 45° |
| 1 | 1.73 | 1.73 | 1.73 | 60° |
Each ratio lands near a special tangent. The protractor is never needed: the tape and the table find the angle.
Sixty degrees gives the shortest shadow, because a steeper light line makes a taller, thinner triangle.
- Read the question.
- Tap your answer.
The light is 30° above the dock and a shadow is 6 m long. How tall is the object? Round to 1 decimal place.| What the lab shows | True or false? |
|---|---|
| The shadow is the side adjacent to the light's angle. | ? |
| A shorter shadow means a smaller angle above the ground. | ? |
| Stick ÷ shadow ≈ 0.58 matches tan 30° = √3/3. | ? |
| The protractor is needed to find the angle in this lab. | ? |
| A taller stick at the same angle makes a longer shadow in the same ratio. | ? |
Careful lab work. Tomorrow the circle shows why cosine is even, sine is odd, and both repeat every turn.