Understanding the Sin of an Angle: θ and 90°

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SUMMARY

The sine of an angle θ is defined as sinθ = p/h, where p is the length of the side opposite the angle and h is the hypotenuse. For θ = 90°, sin90 = 1, indicating that the length of the perpendicular side (p) equals the hypotenuse (h). This creates a contradiction in a right triangle, as the hypotenuse is always the longest side. Visualizing a right triangle with a 90° angle clarifies that one side cannot equal the hypotenuse, reinforcing the fundamental properties of right triangles.

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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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