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Welcome! Today we are going to unlock the secrets of right-angled triangles using three magical ratios: sine, cosine, and tangent.
Imagine you have a right-angled triangle. The sides have special names based on which angle you are looking at: the Hypotenuse (the longest side), the Opposite side (across from your angle), and the Adjacent side (next to your angle).
Sine (or 'sin' for short) is the ratio of the Opposite side to the Hypotenuse. Think of it as a measure of how high the triangle climbs compared to the length of the slope!
Cosine (or 'cos') compares the Adjacent side to the Hypotenuse, while Tangent (or 'tan') compares the Opposite to the Adjacent. An easy way to remember all three is the famous acronym: SOH-CAH-TOA!
Find the value of sin(θ) for a right-angled triangle where the side opposite to angle θ is 3 cm, the adjacent side is 4 cm, and the hypotenuse is 5 cm.
- Identify the formula for sine: sin(θ) = Opposite / Hypotenuse.
- Find the length of the Opposite side from the given values, which is 3 cm.
- Find the length of the Hypotenuse from the given values, which is 5 cm.
- Substitute these values into your formula: sin(θ) = 3 / 5.
- Simplify the fraction or convert it to a decimal: sin(θ) = 0.6.
