**Shadows**

Change of light conditions in different seasons. Measuring height using shadows.

**Nature**

**Keywords**

shadow, light condition, measuring height, winter solstice, summer solstice, path of the Sun, season

**Related items**

### Scenes

- December 21 on the northern hemisphere June 21 on the southern hemisphere
- June 21 on the northern hemisphere December 21 on the southern hemisphere
- March 21 and September 22

- 10 m (32.81 ft)
- 8.3 m (27.23 ft)
- 67.2 m (220.5 ft)
- 81 m (265.7 ft)

We know the **length of both legs** of the **small right-angled triangle**, and **one of the legs** of the **large right-angled triangle**.

In this example, the **ratio** of the **two legs** is: 10 m (32.81 ft) : 8.3 m (27.23 ft)

The **length** of one leg of the **large right-angled triangle** (the length of the shadow) is **known**, while the other (the height of the tower) is **unknown**.

In this example, their **ratio** is: *x* m: 67.2 m (220.5 ft)

The **ratio** of the corresponding **legs of similar triangles** is **equal**:

10 m (32.81 ft) : 8.3 m (27.23 ft) *= **x* m : 67.2 m (220.5 ft)

Therefore*x* = (10 m : 8.3 m or 32.81 ft : 27.23 ft) ∙ 67.2 m (220.5 ft) ≈ 81 m (265.7 ft).

The tower is **approximately** 81 m (265.7 ft) tall.

- 10 m (32.81 ft)
- 8.3 m (27.23 ft)
- 67.2 m (220.5 ft)
- 81 m (265.7 ft)

### Narration

The **winter solstice** marks the **longest night** of the year. After this, days become longer until the **summer solstice**, which marks the **longest day** of the year. In the **Northern Hemisphere**, the **winter solstice** usually occurs on **December 21**. In the **Southern Hemisphere**, it is the **summer solstice** that occurs on this date.

In the **Northern Hemisphere**, the **summer solstice** usually occurs on **June 21**, which is the day the **winter solstice** occurs in the **Southern Hemisphere**.

This animation demonstrates **shadows** in countries located in **Central Europe** or at similar latitudes. As you can see, shadows are **longer** at the time of the **winter solstice** than at the summer solstice, since the apparent path of the **Sun** is **lower** in winter than in summer. In the **Southern Hemisphere**, it is the **other way round**.

The **height of a building** can easily be ascertained with **shadows**. To do this, we need an object of known **height**, then we measure the **length of its shadow**. In this example we know that the height of the **pole** is 10 m (32.81 ft). We measure the length of its **shadow**, then we measure the length of the **tower's shadow**.

We can now **calculate** the **height** of the tower using our knowledge of **similar triangles**.

We know the **lengths of both legs** of the **small triangle**. We also know the length of **one leg** of the **large triangle**. Based on these figures, we can calculate the **length of the other leg**, that is, the height of the **tower**.

Since the two **triangles** are **similar**, the **ratio** of the **lengths** of the corresponding legs is **equal**. That is, the ratio of the pole height to the length of the **shadow** of the pole is **equal** to the ratio of the tower height to the **length** of the tower's **shadow**. Now let's solve the **equation** to find the height of the tower.

### Related items

#### Change of seasons (basic)

Due to the Earth´s tilted axis, the angle of the Sun's rays at given latitudes is continuously changing during the year.

#### Change of seasons (intermediate)

Due to the Earth´s tilted axis, the angle of the Sun's rays at given latitudes continuously changes during the year.

#### Light and shadow

By varying the position of the light source, you can examine the shades projected onto the planes of the coordinate system.

#### Measuring time

The first calendars and time-measuring instruments were already used by ancient Eastern civilizations.

#### Time zones

The Earth is divided into 24 time zones. Standard time is the time used within time zones.

#### Transparency

This animation explains transparency and opacity, the principle of radiography, and the light-absorbing properties of materials.