Mathematics — first biennium · Lesson
Relative to an acute angle α, sine, cosine and tangent are side ratios: opposite/hypotenuse, adjacent/hypotenuse and opposite/adjacent.
Prerequisites: Radians, right triangles and Pythagoras
Goal: Interpret sine, cosine and tangent as ratios between sides relative to an acute angle.
In this lesson: Interpret sine, cosine and tangent as ratios between sides relative to an acute angle.
New concept: In a right triangle, relative to an acute angle θ: sinθ=opposite leg/hypotenuse, cosθ=adjacent leg/hypotenuse, tanθ=opposite leg/adjacent leg. ‘Opposite’ and ‘adjacent’ depend on the chosen angle.
How to proceed: The hypotenuse keeps its name; the two legs are 'opposite' and 'adjacent' only relative to the chosen angle α.
You can already assume: Radians, right triangles and Pythagoras.
Relative to angle α, opposite, adjacent and hypotenuse determine sine, cosine and tangent.
Completed exercises: 0/5 · Correct on first attempt: 0
The hypotenuse keeps its name; the two legs are 'opposite' and 'adjacent' only relative to the chosen angle α.
Data / situation: In the right triangle, the leg adjacent to α is 8, the opposite leg is 15, and the hypotenuse is 17.
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