Understanding the Sin of an Angle: θ and 90°

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The discussion centers on the definition of the sine function, specifically how sin(θ) is expressed as the ratio of the opposite side (p) to the hypotenuse (h) in a right triangle. It highlights that when θ equals 90 degrees, sin(90) equals 1, implying that the length of the perpendicular side (p) equals the hypotenuse (h). This raises a conceptual question about the nature of a right triangle at 90 degrees, where one side would indeed be equal to the hypotenuse. Participants are encouraged to visualize the triangle to better understand this relationship. The conversation ultimately seeks clarity on the geometric implications of these trigonometric principles.
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sin of an angle θ is sinθ=p/h. again sin90=1 which means that p=h.but the hypotenuse is the longest side of a right triangle so how can it be equal to the perpendicular?
 
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anigeo said:
sin of an angle θ is sinθ=p/h. again sin90=1 which means that p=h.but the hypotenuse is the longest side of a right triangle so how can it be equal to the perpendicular?

Step back from the math for a moment and visualize this triangle.

You've got right triangle whose theta is 90 degrees. What does this triangle look like?

Does it make sense that, if its theta is 90, you'd have one side as long as the hypotenuse? Can you intuit how long the other side would be?
 
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