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
| \(\large{ t_a = 2\;b\;c \;\; cos \; \frac { \frac {A}{2} }{ b \;+\; c } }\) | |
| \(\large{ t_a = \sqrt { bc \; \frac { 1 \;-\; a^2 } { \left( b \;+\; c \right)^2 } } }\) | |
| \(\large{ t_b = 2\;a\;c \;\; cos \; \frac { \frac {B}{2} }{ a \;+\; c } }\) | |
| \(\large{ t_b = \sqrt { a\;c \; \frac { 1 \;-\; b^2 } { \left( a \;+\; c \right)^2 } } }\) | |
| \(\large{ t_c = a\;b \; \sqrt { \frac { 2 }{ a \;+\; b } } }\) |
Where:
\(\large{ t_a, t_b, t_c }\) = angle bisector
\(\large{ A, B }\) = angle
\(\large{ a, b, c }\) = edge
Area of a Right Isosceles Triangle formulas
| \(\large{ A_{area} = \frac {h\;b} {2} }\) | |
| \(\large{ A_{area} = \frac {1} {2}\; b\;h }\) | |
| \(\large{ A_{area} = a\;b\; \frac {\sin \;y} {2} }\) |
Where:
\(\large{ A_{area} }\) = area
\(\large{ a, b, c }\) = edge
\(\large{ h }\) = height
Circumcircle of a Right sosceles Triangle formulas
| \(\large{ R = \frac { 1 } { 2 } \; \sqrt { a^2 + b^2 } }\) | |
| \(\large{ R = \frac { H } { 2 } }\) |
Where:
\(\large{ R }\) = outcircle
\(\large{ a, b, c }\) = edge
\(\large{ H }\) = hypotenuse
Height of a Right Isosceles Triangle formula
| \(\large{ h_c = 2\; \frac {A_{area}}{b} }\) |
Where:
\(\large{ h^c }\) = height
\(\large{ A_{area} }\) = area
\(\large{ a, b, c }\) = edge
Inscribed Circle of a Right Isosceles Triangle formula
| \(\large{ r = \frac { a \;+\; b \;-\; c } { 2 } }\) |
Where:
\(\large{ r }\) = incircle
\(\large{ a, b, c }\) = edge
Median of a Right Isosceles Triangle formulas
| \(\large{ m_a = \sqrt { \frac { 4\;b^2 \;+\; a^2 }{ 2 } } }\) | |
| \(\large{ m_b = \sqrt { \frac { 4\;a^2 \;+\; b^2 }{ 2 } } }\) | |
| \(\large{ m_c = \frac {c} {2} }\) |
Where:
\(\large{ m_a, m_b, m_c }\) = median
\(\large{ a, b, c }\) = edge
Perimeter of a Right Isosceles Triangle formula
| \(\large{ P = a + b + c }\) |
Where:
\(\large{ P }\) = perimeter
\(\large{ a, b, c }\) = edge
Side of a Right Isosceles Triangle formula
| \(\large{ a = P - b - c }\) | |
| \(\large{ a = 2\; \frac {A_{area}} {b\;\sin y} }\) | |
| \(\large{ b = P - a - c }\) | |
| \(\large{ b = 2\; \frac {A_{area}}{h} }\) | |
| \(\large{ c = P - a - b }\) |
Where:
\(\large{ a, b, c }\) = edge
\(\large{ A_{area} }\) = area
\(\large{ P }\) = perimeter
Trig Functions
- Find A
- given a c : \(\; sin \; A= a \div c \)
- given b c : \(\; cos \; A= b \div c \)
- given a b : \(\; tan \; A= a \div b \)
- Find B
- given a c : \(\; sin \; B= a \div c \)
- given b c : \(\; cos \; B= b \div c \)
- given a b : \(\; tan \; B= b \div a \)
- Find a
- given A c : \(\; a= c*sin \; A \)
- given A b : \(\; a= b*tan \; A \)
- Find b
- given A c : \(\; b= c*cos \; A \)
- given A a : \(\; b= a \div tan \; A \)
- Find c
- given A a : \(\; c= a \div sin \; A \)
- given A b : \(\; c= b \div cos \; A \)
- given a b : \(\; c= \sqrt { a^2+b^2 } \)
- Find Area
- given a b : \(\; Area= a\;b \div 2 \)