Right Isosceles Triangle

Right isosceles triangle (a two-dimensional figure) has one side a right 90° interior angle and the other two angles are 45°.
Angle bisector of a right isosceles 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.
Hypotenuse of a right isosceles triangle is the longest side or the side opposite the right angle.
Inscribed circle is the Iargest circle possible that can fit on the inside of a two-dimensional figure.
Median of a right isosceles triangle is a line segment from a vertex (coiner point) to the midpoint of the opposite side.
Semiperimeter is one half of the perimeter.
Side of a right triangle is one half of the perimeter.
Two sides are congruent.
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 (corner 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 Isosceles 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
$t_a, t_b, t_c$ = angle bisector	$in$	$mm$
$A, B, C$ = angle	$deg$	$rad$
$a, b, c$ = edge	$in$	$mm$

Area of a Right Isosceles Triangle formulas
$A_{area} \;=\; \dfrac{ h \cdot b }{2}$ $A_{area} \;=\; \dfrac{1}{2} \cdot b \cdot h$ $A_{area} \;=\; a \cdot b \cdot \dfrac{ sin( y) }{ 2 }$
Symbol	English	Metric
$A_{area}$ = area	$in^2$	$mm^2$
$a, b, c$ = edge	$in$	$mm$
$h$ = height	$in$	$mm$

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

Height of a Right Isosceles Triangle formula
$h_c \;=\; 2 \cdot \dfrac{ A_{area} }{ b }$
Symbol	English	Metric
$h^c$ = height	$in$	$mm$
$A_{area}$ = area	$in^2$	$mm^2$
$a, b, c$ = edge	$in$	$mm$

Inscribed Circle of a Right Isosceles Triangle formula
$r \;=\; \dfrac{ a + b - c }{ 2 }$
Symbol	English	Metric
$r$ = incircle	$in$	$mm$
$a, b, c$ = edge	$in$	$mm$

Median of a Right Isosceles 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
$m_a, m_b, m_c$ = median	$in$	$mm$
$a, b, c$ = edge	$in$	$mm$

Perimeter of a Right Isosceles Triangle formula
$P \;=\; a + b + c$
Symbol	English	Metric
$P$ = perimeter	$in$	$mm$
$a, b, c$ = edge	$in$	$mm$

Side of a Right Isosceles Triangle formula
$a \;=\; P - b - c$ $a \;=\; 2\cdot \dfrac{A_{area} }{ b \cdot sin( y) }$ $b \;=\; P - a - c$ $b \;=\; 2 \cdot \dfrac{A_{area} }{ h}$ $c \;=\; P - a - b$
Symbol	English	Metric
$a, b, c$ = edge	$in$	$mm$
$A_{area}$ = area	$in^2$	$mm^2$
$P$ = perimeter	$in$	$mm$

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 : $\; Area \;=\;\dfrac{ a \cdot b }{ 2 }$