TwiddleLab / Math / Trig and Waves

Right Triangles and Ratios

Lesson 1 of 11 · 5 min · Free, no account needed

What you will learn

• In a right triangle with angle A, sin A = opposite ÷ hypotenuse, cos A = adjacent ÷ hypotenuse, tan A = opposite ÷ adjacent.
• The ratios depend only on the angle, not on the size: a 30° ramp always has height ÷ slope = 0.5.
• Know one side and the angle, and the ratios give you the other sides.

Start the lesson

How the lesson goes

1. How steep is too steep for a skate ramp?

   One number tells you. First a bet: which of these two ramps is steeper?

2. Stretch the 30° ramp.

   Drag the top corner. The sides change. Watch the height ÷ slope card.

3. Each angle has its own ratio. Find three.

   Turn the angle lever until height ÷ slope hits the target.

4. Three ratios, three names.

   Seen from angle A, the side across is opposite, the side next to A is adjacent, the long side is the hypotenuse.

   sin A = opposite ÷ hypotenuse. Your height ÷ slope was the sine.

   cos A = adjacent ÷ hypotenuse and tan A = opposite ÷ adjacent. Some people remember SOH CAH TOA.

5. Make the ratio card for the 3-4-5 ramp.

   Fill sin A, cos A and tan A with the side lengths.

   Opposite 3, adjacent 4, hypotenuse 5. sin = 3/5 = 0.6, cos = 4/5 = 0.8, tan = 3/4 = 0.75.

6. Game: three ramp orders, same angle as your card.

   Each order gives one side. Set the lever to the side asked for and press Build.

7. sin, cos and tan: one angle, three fixed ratios.

   Pick your own ramp angle and ride it. The card shows its three ratios.

Next lesson: The Unit Circle Clock · Part of the course: Trig and Waves

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