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Eclipse geometry activities for IGCSE and GCSE

A ready-to-teach lesson on the geometry of eclipses: why the Moon can only just cover the Sun. A 5-minute starter, a 35-minute main activity on ratio, similar triangles and angles, an extension and full worked answers. Use it any time, or when an eclipse is in the news.

Level
IGCSE and GCSE (Higher and Extended)
Time
40 minutes, plus a 10-minute extension
Topics
Standard form; Similar triangles and ratio; Trigonometry: tan and angles of elevation
Equipment
The starter is non-calculator. A calculator is needed for the main activity.

Download student sheet (PDF)Answers (PDF)

Suggested timings

PartTimeWhat
Starter5 minQuick questions on the board
Main: task A12 minWhy the Moon just covers the Sun
Main: task B12 minAngles with tan
Main: task C11 minA pinhole viewer
Extension10 minFast finishers or homework

Starter (5 minutes)

No calculator.

  1. Write 1 400 000 in standard form.
  2. Write 3500/1 400 000 as a fraction in its simplest form.
  3. A 1.8 m person casts a 2.4 m shadow. At the same time a tree casts a 12 m shadow. How tall is the tree?
  4. Write down tan 45°.

Main activity (35 minutes)

Task A: Why the Moon just covers the Sun (12 min)

Take these rounded values: Sun diameter 1 400 000 km at 150 000 000 km from us; Moon diameter 3500 km at 380 000 km.

  1. How many times wider is the Sun than the Moon?
  2. How many times further away is the Sun than the Moon? Give 3 significant figures.
  3. Use similar triangles to find the distance at which the Moon would exactly cover the Sun.

Task B: Angles with tan (12 min)

Half of the Moon’s width and its distance make a right-angled triangle, so the angle the Moon fills is 2 × tan−1(1750 ÷ 380 000).

  1. Find the angle the Moon fills, in degrees, to 3 significant figures.
  2. Find the angle the Sun fills, in degrees, to 3 significant figures, using 2 × tan−1(700 000 ÷ 150 000 000).
  3. When the Sun’s angle of elevation is 40°, a tree casts a shadow 12 m long. Find the height of the tree, to 3 significant figures.

Task C: A pinhole viewer (11 min)

Never look at the Sun. A pinhole in a card makes a safe image of the Sun on a screen behind it. The image and the Sun make similar triangles with the pinhole.

  1. The screen is 1 m behind the pinhole. Find the width of the image, in mm, to 3 significant figures.
  2. The screen is moved to 2 m behind the pinhole. Find the width of the image, to 3 significant figures.
  3. How far behind the pinhole must the screen be for an image 2 cm wide? Give your answer in metres, to 3 significant figures.

Extension (10 minutes)

For fast finishers, or as homework.

  1. Write 150 000 000 ÷ 380 000 in standard form, to 3 significant figures, and explain what it tells you.

For teachers

Teacher notes and full worked answers
  • Safety first: never look at the Sun directly, even during an eclipse. A pinhole viewer (task C) is a safe way to see it.
  • Every physical value is a rounded value given in the question; the real values vary.
  • Task A is the big idea: 400 times wider and about 400 times further away is why the Moon can just cover the Sun.

Starter

  1. 1.4 × 106
    • 1 400 000 = 1.4 × 1 000 000
  2. 1/400
    • 1 400 000 ÷ 3500 = 400
  3. 9 m
    • 12 ÷ 2.4 = 5, and 1.8 × 5 = 9
  4. 1
    • Opposite = adjacent in a right-angled isosceles triangle.

Task A: Why the Moon just covers the Sun

  1. 400 times
    • 1 400 000 ÷ 3500 = 400
  2. 395 times
    • 150 000 000 ÷ 380 000 = 394.7…
  3. 375 000 km
    • Distance ÷ 3500 = 150 000 000 ÷ 1 400 000
    • Distance = 3500 × 150 000 000 ÷ 1 400 000 = 375 000 km

Task B: Angles with tan

  1. 0.528°
    • tan−1(1750 ÷ 380 000) = 0.2638…°
    • × 2 = 0.5277…°
  2. 0.535°
    • 2 × tan−1(0.004666…) = 0.5347…°
  3. 10.1 m
    • height = 12 × tan 40° = 10.06…

Task C: A pinhole viewer

  1. 9.33 mm
    • Image ÷ 1000 mm = 1 400 000 ÷ 150 000 000
    • Image = 9.333… mm
  2. 18.7 mm
    • Twice the distance gives twice the width: 18.66… mm
  3. 2.14 m
    • 20 mm ÷ 9.333… mm per metre = 2.142… m

Extension

  1. 3.95 × 102: the Sun is about 395 times further away
    • 150 000 000 ÷ 380 000 = 394.7… = 3.95 × 102 (3 s.f.)
    • The Sun is 400 times wider but only about 395 times further away, so it looks very slightly bigger.

The same answers are in the answers PDF. Every answer was recomputed by computer before publishing.

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