## Right Triangle Congruence

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a squared plus b squared equals c squared, this is use to find missing sides of a triangle c= hypotenuse or the longest leg

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A right-angled triangle is a triangle in which one of the angles is a right-angle. The hypotenuse of a right angled triangle is the longest side, which is the one opposite the right angle. The adjacent side is the side which is between the angle in question and the right angle. The opposite side is opposite the angle in question.
In any right angled triangle, for any angle:
The sine of the angle = the length of the opposite side
the length of the hypotenuse
The cosine of the angle = the length of the adjacent side
the length of the hypotenuse
The tangent of the angle = the length of the opposite side
the length of the adjacent side
So in shorthand notation:

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In a right triangle where theta is given and a side is given you can solve for anything.
To solve for the hypotenuse use the phrase SOH CAH TOA.
If the angle and the opposite are given use opposite side divided by sin of the angle. and vice versa for all other sides and angles.
Soh cah toa stands for
Sin opposite over Hypotenuse
Cosin adjacent over hypotenuse
Toa opposite over adjacent
all of these are with respect to theta.

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Sin Cos and Tan are very important.
Soh(sin,opp, hypotenuse)-Coh(can,opp,hypotenuse)-Toa(Tan,opp, adjacent)

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There are three sides in a triangle. Each side is designated A and B--the legs of the triangle--or the shortest sides.
The longest side is attributed C--hypotenuse.
A^2+b^2=c^2

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a^2+b^2=c^2
This theorem can only be used with right triangles. A and B are the leags and C is the hypotenuse.

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The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the Pythagorean equation:[1]
A^2+B^2=C^2
where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.

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For use with triangles, the theorem is that A Squared + B squared = C squared. C represents the Hypotenuse and A/B represent the other two legs.

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Definition
The longest side of the triangle is called the "hypotenuse", so the formal definition is:
In a right angled triangle the square of the hypotenuse is equal to
the sum of the squares of the other two sides.
So, the square of a (a²) plus the square of b (b²) is equal to the square of c (c²):
a2 + b2 = c2
Sure ... ?
Let's see if it really works using an example. A "3,4,5" triangle has a right angle in it, so the formula should work.
Let's check if the areas are the same:
32 + 42 = 52
Calculating this becomes:
9 + 16 = 25
Yes, it works !
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