Right Triangle

Right triangle (a two-dimensional figure) has one side a right 90° interior angle.
The other two angles are unequal and no sides are equal.
Angle bisector of a right triangle is a line that splits an angle into two equal angles.
Circumcircle is a circle that passes through all the vertices of a two-dimensional figure.
Height of a right triangle is the length of the two sides and the perpendicular height of the 90 degree angle.
Hypotenuse of a right triangle is the longest side or the side opposite the right angle.
Inscribed circle is the largest circle possible that can fit on the inside of a two-dimensional figure.
Median of a right triangle is a line segment from a vertex (coiner point) to the midpoint of the opposite side.
Semiperimeter is one half of the perimeter.
3 edges
3 vertexs
a = opposite leg
b = adjacent leg
c = hypotenuse
Angles: ∠A, ∠B, ∠C
Height: \(h_a\), \(h_b\), \(h_c\)
Median: \(m_a\), \(m_b\), \(m_c\) - A line segment from a vertex (coiner point) to the midpoint of the opposite side
Angle bisectors: \(t_a\), \(t_b\), \(t_c\) - A line that splits an angle into two equal angles

Angle bisector of a Right Triangle formulas
\( t_a \;=\; 2 \cdot b \cdot c \cdot cos \left( \dfrac{ \dfrac{A}{2} }{ b + c } \right) \) \( t_a \;=\; \sqrt{ b\cdot c \cdot \dfrac{ 1 - a^2 }{ \left( b + c \right)^2 } } \) \( t_b \;=\; 2\cdot a\cdot c \cdot cos \left( \dfrac{ \dfrac{B}{2} }{ a + c } \right) \) \( t_b \;=\; \sqrt{ a\cdot c \cdot \dfrac{ 1 - b^2 }{ \left( a + c \right)^2 } } \) \( t_c \;=\; a\cdot b \cdot \sqrt{ \dfrac{ 2 }{ a + b } } \)
Symbol	English	Metric
\(\large{ t_a, t_b, t_c }\) = angle bisector	\(\large{ in}\)	\(\large{ mm}\)
\(\large{ A, B, C }\) = angle	\(\large{deg}\)	\(\large{rad}\)
\(\large{ a, b, c }\) = edge	\(\large{ in}\)	\(\large{ mm }\)

Area of a Right Triangle formula
\( A_{area} = \dfrac{ a \cdot b }{ 2 } \)
Symbol	English	Metric
\(\large{ A_{area} }\) = area	\(\large{ in}\)	\(\large{ mm}\)
\(\large{ a, b, c }\) = edge	\(\large{ in}\)	\(\large{ mm }\)

Circumcircle of a Right Triangle formulas
\( R \;=\; \dfrac{ 1 }{ 2 } \cdot \sqrt { a^2 + b^2 } \) \( R \;=\; \dfrac{ H }{ 2 } \)
Symbol	English	Metric
\(\large{ R }\) = outcircle	\(\large{ in}\)	\(\large{ mm}\)
\(\large{ a, b, c }\) = edge	\(\large{ in}\)	\(\large{ mm }\)
\(\large{ H }\) = hypotenuse	\(\large{ in}\)	\(\large{ mm }\)

Height of a Right Triangle formulas
\( h_a \;=\; b \) \( h_b \;=\; a \) \( h_c \;=\; \dfrac{ a \cdot b }{ c} \)
Symbol	English	Metric
\(\large{ h_a, h_b, h_c }\) = hight	\(\large{ in}\)	\(\large{ mm}\)
\(\large{ a, b, c }\) = edge	\(\large{ in}\)	\(\large{ mm }\)

Hypotenuse of a Right Triangle formula
\( c \;=\; \sqrt{ a^2 + b^2} \)
Symbol	English	Metric
\(\large{ c }\) = hypotenuse (H)	\(\large{ in}\)	\(\large{ mm}\)
\(\large{ a, b, c }\) = edge	\(\large{ in}\)	\(\large{ mm }\)

Inscribed Circle of a Right Triangle formulas
\( r \;=\; \dfrac{ a\cdot b }{ a + b + c } \) \( r \;=\; \dfrac{ a + b - c }{ 2 } \)
Symbol	English	Metric
\(\large{ r }\) = incircle	\(\large{ in}\)	\(\large{ mm}\)
\(\large{ a, b, c }\) = edge	\(\large{ in}\)	\(\large{ mm }\)

Median of a Right Triangle formulas
\( m_a \;=\; \sqrt{ \dfrac{ 4\cdot b^2 + a^2 }{ 2 } } \) \( m_b \;=\; \sqrt{ \dfrac{ 4\cdot a^2 + b^2 }{ 2 } } \) \( m_c \;=\; \dfrac{c }{ 2} \)
Symbol	English	Metric
\(\large{ m_a, m_b, m_c }\) = median	\(\large{ in}\)	\(\large{ mm}\)
\(\large{ a, b, c }\) = edge	\(\large{ in}\)	\(\large{ mm }\)

Perimeter of a Right Triangle formulas
\( P \;=\; a + b + c \) \( P \;=\; a + b + \sqrt{a^2 + b^2 } \)
Symbol	English	Metric
\(\large{ P }\) = perimeter	\(\large{ in}\)	\(\large{ mm}\)
\(\large{ a, b, c }\) = edge	\(\large{ in}\)	\(\large{ mm }\)

Semiperimeter of a Right Triangle formula
\( s \;=\; \dfrac{ a + b + c }{ 2 } \)
Symbol	English	Metric
\(\large{ s }\) = semiperimeter	\(\large{ in}\)	\(\large{ mm}\)
\(\large{ a, b, c }\) = edge	\(\large{ in}\)	\(\large{ mm }\)

Trig Functions
Find A given a c : \(\; sin( A) \;=\; \dfrac{ a }{ c }\) given b c : \(\; cos( A) \;=\; \dfrac{ b }{ c }\) given a b : \(\; tan( A) \;=\; \dfrac{ a }{ b }\)
Find B given a c : \(\; sin( B) \;=\; \dfrac{ a }{ c }\) given b c : \(\; cos( B) \;=\; \dfrac{ b }{ c }\) given a b : \(\; tan( B) \;=\; \dfrac{ b }{ a }\)
Find a given A c : \(\; a \;=\; c \cdot sin( A) \) given A b : \(\; a \;=\; b \cdot tan( A) \)
Find b given A c : \(\; b \;=\; c \cdot cos( A) \) given A a : \(\; b \;=\; \dfrac{ a }{ tan( A) }\)
Find c given A a : \(\; c \;=\; \dfrac{ a }{ sin( A) }\) given A b : \(\; c \;=\; \dfrac{ b }{ cos( A) }\) given a b : \(\; c \;=\; \sqrt{ a^2 + b^2 } \)
Find Area given a b : \(\; Area \;=\; \dfrac{ a\cdot b }{ 2 }\)