Finding the angle
A pole stands upright. Its shadow lies on the ground. The sun's ray makes an angle with the ground. You can find that angle from the two lengths.
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- A 10 m pole casts a shadow 10√3 m long.
- The sun's ray closes a right triangle. Mark the sun's angle.
- The pole is opposite. The shadow is adjacent. Divide.
- The value 1/√3 belongs to 30°.
From two lengths to an angle
The pole and the shadow are two sides of a right triangle. The pole is opposite the sun's angle. The shadow is adjacent to the sun's angle.
Rule: tan of the angle = height ÷ shadow.
Divide the two lengths. Then match the answer to a value you know. Here the angle is 30°, 45° or 60°.
| height ÷ shadow | Angle |
|---|---|
| 1/√3 | 30° |
| 1 | 45° |
| √3 | 60° |
Take a 10 m pole with a shadow 10√3 m long. Then tan of the sun's angle = 10 ÷ 10√3 = 1/√3. The table says tan 30° = 1/√3. So the sun's angle is 30°.
A shadow as long as the pole gives tan = 1. So the angle is 45°.
Watch out!
Put the height on top. A shadow longer than the pole means a low sun. So height ÷ shadow is less than 1.