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Isosceles Right Triangle

An isosceles right triangle is a triangle with two 45° angles, a right angle and two equal sides. The side opposite the right angle is the base and the two equal angles are the base angles. The ratio of the sides opposite the two 45° angles is 1:1.

Isosceles right triangle is the product of an  isosceles triangle and a right triangle.

The three sides of the isosceles right triangle correspond to the following three sides of a right triangle:
  1. Opposite
  2. Adjacent
  3. Hypotenuse
The three sides are equal to the three persons of the Blessed Trinity as follows:

Opposite = Father (First Person)
Adjacent = Son (Second Person)
Hypotenuse = Holy Spirit (Third Person)

The linear magnitude of each person of the Blessed Trinity can be calculated via any of the six trigonometric ratios if either the angle facing the opposite side or the angle facing the adjacent side is known.

Let the angle facing the opposite side be Y. The side opposite the right angle is the hypotenuse and the remaining side is the adjacent. 

Therefore we can calculate angle Y via any of the following three of the six trigonometric ratios:

Sin Y = Opp/Hyp
Cos Y = Adj/Hyp
Tan Y = Opp/Adj

Where,

Sin = Sine
Cos = Cosine
Tan = Tangent
Opp = Opposite
Adj = Adjacent
Hyp = Hypotenuse

A side of the right triangle can be calculated via Pythagorean theorem if the other two sides are known.

Pythagorean theorem states that the square of the hypotenuse of a right triangle (a right-angled triangle) is equal to the sum of the square of the opposite side and the square of the adjacent side.

|Hyp|² = |Opp|² + |AdJ|² (Pythagorean theorem)

Since the Father is one person, Opp (the vertical line) is equal to 1. And since the Son is one person, Adj (the horizontal line) is equal to 1. The Holy Spirit is the Hypotenuse whose magnitude is calculated via Pythagorean theorem as follows:

Opp (Son) = 1
Adj (Father) = 1

Substituting 1 and 1 into the Pythagorean theorem,
|Hyp|² = 1² + 1²
          = 1 + 1
          = 2

Hyp = 2

Therefore the isosceles right triangle is a right-angled triangle whose opposite and adjacent sides are equal or an isosceles triangle that has a right angle.

The angle Y facing the opposite side and the angle X facing the adjacent side can be calculated via Sin Y = Opp/Hyp and Sine X = Opp/Hyp.

Opp = 1 (Father)

Hyp = 2

Sin Y  = Father/Holy Spirit
           = 1/2
       Y = 45°


Opp = 1 (Son)

Sin X = Son/Holy Spirit
          = 1/2
       X = 45°

This means that the base angles of the isosscles right triangle are equal to 45°.

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