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Right Isosceles Triangle

 

right isosceles triangle 2

right isosceles triangle 4t

right isosceles triangle 3

  • 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 :  \(\; Area \;=\;\dfrac{  a \cdot b }{ 2 }\)

 

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