This is an isosceles right triangle because sides a and b (the height and the base) are the same lengths with two of the angles being 45 degrees adding up to a total with the right angle of 180 degrees (all triangles have angles that add up to 180 degrees). I just want to know from this triangle or any other right triangles why the hypotenuse is the longest side. You"ll really be helping me out.

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asked Oct 26 "14 at 2:17

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Let $a$ be the hypotenuse and $b,c$ the others sides, then by Pythagorean Theorem$$a^2=b^2+c^2.$$Then$$a^2>b^2,quad a^2>c^2.$$Therefore$$a>bquad a>c.$$

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answered Oct 26 "14 at 2:20

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Alternatively, you have the law of sines: For any triangle with sides, $A,B,C$ and corresponding angles $a,b,c$ with angle $a$ opposite side $A$ et cetera, you have the following:

$$fracsin aA = fracsin bB = fracsin cC$$

Let $a$ be $90$ degrees, making $A$ our hypotenuse. Since $a+b+c = 180$ and we don"t want to consider negative angles or angles equal to zero in a triangle, we have that $b

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