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Author Topic: Explain why the sine of an acute angle cannot be greater than 1?  (Read 1917 times)
MathTutor
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« on: April 19, 2009, 02:19:11 AM »
Question:
Explain why the sine of an acute angle cannot be greater than 1?

Answer:
sine of an acute angle= O/H, where O =opposite, H=hypothenuse.
The proof is by contraction.
Suppose that sine>1, then O/H>1 or O>H.
But O<H which leads to a contradiction.
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Rishta
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« Reply #1 on: April 19, 2009, 03:07:29 AM »
The sine of an angle is obtained by dividing the side opposite to the angle by the hypotenuse (the longest side).
A triangle contains only 3 sides, the hypotenuse being the longest.
Thus, opposite/hypotenuse must in all possible conditions be less than 1.
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