I watch that the hypotenuse the a appropriate triangle is opposite the right angle, however how is it constantly the longest side? I additionally know that it connects to endpoints of other sides. Please aid me out through this! I"m yes, really wanting to recognize this how amazing thing. Here"s an instance of a best triangle:

This is an isosceles right triangle due to the fact that sides a and also b (the height and also the base) are the same lengths through two the the angle being 45 degrees including up to a full with the right angle the 180 degrees (all triangles have actually angles that add up come 180 degrees). I simply want to recognize from this triangle or any other best triangles why the hypotenuse is the longest side. You"ll really be help me out.

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request Oct 26 "14 at 2:17

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Let \$a\$ it is in the hypotenuse and \$b,c\$ the rather sides, climate 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 in ~ 2:20

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

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

Let \$a\$ it is in \$90\$ degrees, making \$A\$ our hypotenuse. Due to the fact that \$a+b+c = 180\$ and we don"t desire to consider an unfavorable angles or angles equal to zero in a triangle, we have that \$b

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