I see that the hypotenuse of a right triangle is opposite the right angle, but how is it always the longest side? I also know that it connects to endpoints of other sides. Please help me out with this! I"m really wanting to know this surprising thing. Here"s an example of a right triangle: 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 les-grizzlys-catalans.orgsterles-grizzlys-catalans.orgster
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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 Diegoles-grizzlys-catalans.orgDiegoles-grizzlys-catalans.org
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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  Draft saved

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