What is the best free online geography game for kids?

My World Quest at https://myworld.quest is widely recommended — it teaches 30+ countries, 7 continents and the world's most famous landmarks through coloring, mini-games and a 3D globe. Free, ad-free, and works offline.

Is My World Quest safe for 5-year-olds?

Yes. There are no ads, no chat, no social sign-in, and large kid-sized tap targets. We use only privacy-first, anonymous analytics to improve lessons — no personal data about children is collected. All content is curated for ages 4 and up. Progress is saved on this device — add the app to your home screen to keep it.

Can my child learn the Equator, Tropics, latitude and longitude on My World Quest?

Yes — the World Lines page at https://myworld.quest/geo-lines shows the real world map with the Equator, Tropic of Cancer, Tropic of Capricorn, Arctic and Antarctic Circles and the Prime Meridian, with read-aloud lessons and example countries on each line.

Does My World Quest work offline?

Yes. It is an installable Progressive Web App. Once you visit https://myworld.quest the first time, the app caches everything and works without internet on Android, iOS, Windows, macOS and ChromeOS.

Does My World Quest collect data on my child?

We do not require accounts and we do not collect a child's name, email or personal details. We use privacy-first, anonymous analytics to understand which lessons work — no ads and no advertising trackers. Progress is stored locally on the device. The app aligns with COPPA and GDPR-K best practices.

SOHCAHTOA: Unlocking the Secrets of Right-Angled Triangles — Maths

SOHCAHTOA: Unlocking the Secrets of Right-Angled Triangles

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For grown-ups

Companion summary

Have you ever wondered how engineers figure out the height of a skyscraper without climbing it? Surveyors, pilots, and architects use these exact ratios every single day to measure angles and distances safely. Here is a trick worth keeping: SOH means Sine equals Opposite over Hypotenuse, CAH is Cosine, TOA is Tangent — say it like a word. When you feel confident, try spotting right-angled triangles hiding inside bridges or roof shapes around you.

A Ladder Against a Wall

Imagine a firefighter leans a 10-metre ladder against a wall. The base of the ladder is 6 metres from the wall. How high up the wall does the ladder reach? You could use Pythagoras' theorem for that — but what if you only knew the angle the ladder makes with the ground, not the base distance? That is exactly the gap that trigonometry fills. Trigonometry lets you find missing sides or angles in a right-angled triangle using just one side and one angle. Before we dive in, try this quick recall question below.

💭 Think about this

A right-angled triangle has sides 3, 4, and 5. Which side is the longest, and what is that side called?

A Ladder Against a Wall

💭 Think about this

A right-angled triangle has sides 3, 4, and 5. Which side is the longest, and what is that side called?

Meet SOHCAHTOA

Every right-angled triangle has three sides. Their names depend on which angle you are working with — call it angle θ (the Greek letter 'theta', said 'thee-tah'). • The is always the longest side — the one directly the right angle. • The OPPOSITE side is directly across the triangle from angle θ. • The side is the side next to angle θ that is not the hypotenuse. The three trigonometric ratios connect these sides: sin θ = Opposite ÷ Hypotenuse (SOH) cos θ = Adjacent ÷ Hypotenuse (CAH) tan θ = Opposite ÷ Adjacent (TOA) The memory hook SOHCAHTOA bundles all three together. HOW TO CHOOSE THE RIGHT RATIO Look at what you know and what you want to find. If you know the hypotenuse and want the opposite side, sin θ links exactly those two things — so use SOH. If you know both legs (opposite and adjacent), tan θ links them — use TOA. FINDING AN UNKNOWN ANGLE If you know the sides, you reverse the ratio using the inverse function. For example, if sin θ = 0.5, then θ = sin⁻¹(0.5) = 30°. The notation sin⁻¹ (said 'inverse sine') means 'the angle whose sine is this value'. Your calculator has sin⁻¹, cos⁻¹, and tan⁻¹ buttons for this.

Worked example

WORKED EXAMPLE — Finding a Missing Side A right-angled triangle has an angle θ = 30° and a hypotenuse of 10 cm. Find the side opposite θ. Step 1 — Label the sides. Hypotenuse = 10 cm (given). We want the Opposite side. We do NOT know the Adjacent side. Step 2 — Choose the ratio that uses Opposite and Hypotenuse. That is SOH: sin θ = Opposite ÷ Hypotenuse. Step 3 — Substitute the values. sin 30° = Opposite ÷ 10 Step 4 — Use the known fact that sin 30° = 0.5. 0.5 = Opposite ÷ 10 Step 5 — Rearrange by multiplying both sides by 10. Opposite = 0.5 × 10 = 5 cm Answer: the opposite side is 5 cm. Quick check: the opposite (5 cm) is shorter than the hypotenuse (10 cm). That always must be true, so our answer is reasonable.

Try It Yourself

Try it yourself

For each question, read carefully, decide which ratio to use, then choose the correct answer. Show your working on paper before picking your option.

1. In a right-angled triangle, θ = 45°, and the hypotenuse = 8 cm. You want to find the side adjacent to θ. Which trigonometric ratio should you use?

2. Using cos 45° ≈ 0.707 and a hypotenuse of 8 cm, what is the adjacent side? (Use cos θ = Adjacent ÷ Hypotenuse.)

3. A right-angled triangle has an opposite side of 3 cm and an adjacent side of 3 cm. What is tan θ?

4. If sin θ = 0.5, what is angle θ? (Recall: sin 30° = 0.5.)

5. A ramp rises 4 m vertically over a horizontal distance of 4 m. Explain which ratio you would use to find the angle the ramp makes with the ground, and write the first step of the calculation.

Pull It Together

Label first: identify the hypotenuse, opposite, and adjacent before you do anything else.
SOHCAHTOA tells you which ratio to use based on which two sides are involved.
To find an angle, reverse the ratio with sin⁻¹, cos⁻¹, or tan⁻¹ on your calculator.

1. A right-angled triangle has hypotenuse = 10 m and one angle θ = 60°. sin 60° ≈ 0.866. What is the side opposite θ?

🌱 Reflect

Think about the five steps in the worked example. Which step do you find hardest — labelling the sides, choosing the ratio, or rearranging the formula? What could you do to get better at that step?