Sine, Cosine and Tangent Explained Simply
In a right triangle, sine, cosine and tangent describe how the sides relate to an angle α. With them you can calculate sides and angles without measuring them directly.
đź’¬ Mia asks Grandpa Theo
How do I remember which side is opposite and which is adjacent?
Look at the angle α you're focusing on: the green side directly across from it is the opposite. The blue side right next to it, that isn't the hypotenuse, is the adjacent. The red hypotenuse is always the longest side, across from the right angle.
What's this actually used for in real life?
For example, to calculate heights you can't measure directly - like a tree's height, if you only know the angle to its top and your distance from it!
Show me an example!
A tree casts a 20m shadow when the sun is at a 30° angle. The height is then Adjacent × tan(30°) = 20 × 0.577 ≈ 11.5 meters.
A ladder (hypotenuse) is 5m long and leans at 60° to the ground. How high does it reach?
Answer: Opposite = 5 × sin(60°) = 5 × 0.866 ≈ 4.33m
You'll find sin, cos and tan values on a calculator (SIN/COS/TAN keys) - you only need to memorize a few standard angles like 30°, 45° and 60°.
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