Answer:
Step-by-step explanation:
45-45-90 Rule:
When you have a right angle triangle where one of the acute angles is 45 degrees, the other acute angle must also extend 45 degrees (to satisfy the property that the sum of all angles in a triangle must add to 180 degrees).
Now, a triangle with two equal angles, is an isosceles triangle because the sides opposite the similar angles must be equal in length. In such case, when you use the Pythagorean theorem for right angle triangles, the two legs (X) of the triangle are equal, and it reduces to a very simple form in terms of the hypotenuse (H):
[tex]H=\sqrt{X^2+X^2} \\H=\sqrt{2X^2}\\H=\sqrt{2} \, X[/tex]
30-60-90 Rule:
In this case, the three sides of the right triangle are of different sizes, but are related to the hypotenuse (H) via the well known value of the sine of 30 degrees and of 60 degrees.
Side X (shorter leg, opposite to the 30 degree angle) is exactly half of the hypotenuse's length:
[tex]X = \frac{H}{2}[/tex]
Side Y (the leg opposite the 60 degree angle) equals half of the hypotenuse multiplied by square root of 3:
[tex]Y=\frac{\sqrt{3} }{2} \,H[/tex]
So, as you see it is very easy to find a side or the triangle's hypotenuse by knowing the length of one of them.
