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 |
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\(\large{ t_a = 2\;b\;c \; cos \; \frac { \frac {A}{2} }{ b \;+\; c } }\) \(\large{ t_a = \sqrt { b\;c \; \frac { 1 \;-\; a^2 } { \left( b \;+\; c \right)^2 } } }\) \(\large{ t_b = 2\;a\;c \; cos \; \frac { \frac {B}{2} }{ a \;+\; c } }\) \(\large{ t_b = \sqrt { a\;c \; \frac { 1 \;-\; b^2 } { \left( a \;+\; c \right)^2 } } }\) \(\large{ t_c = a\;b \; \sqrt { \frac { 2 }{ a \;+\; b } } }\) |
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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 |
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\(\large{ A_{area} = \frac {a\;b} {2} }\) | ||
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 |
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\(\large{ R = \frac { 1 } { 2 } \; \sqrt { a^2 + b^2 } }\) \(\large{ R = \frac { H } { 2 } }\) |
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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 |
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\(\large{ h_a = b }\) \(\large{ h_b = a }\) \(\large{ h_c = \frac {a \;b} {c} }\) |
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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 |
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\(\large{ c = \sqrt{a^2+b^2} }\) | ||
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 |
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\(\large{ r = \frac { a\;b } { a \;+\; b \;+\; c } }\) \(\large{ r = \frac { a \;+\; b \;-\; c } { 2 } }\) |
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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 |
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\(\large{ m_a = \sqrt { \frac { 4\;b^2 \;+\; a^2 }{ 2 } } }\) \(\large{ m_b = \sqrt { \frac { 4\;a^2 \;+\; b^2 }{ 2 } } }\) \(\large{ m_c = \frac {c} {2} }\) |
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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 |
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\(\large{ P = a + b + c }\) \(\large{ P = a + b + \sqrt {a^2 + b^2 } }\) |
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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 |
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\(\large{ s = \frac { a \;+\; b \;+\; c } { 2 } }\) | ||
Symbol | English | Metric |
\(\large{ s }\) = semiperimeter | \(\large{ in}\) | \(\large{ mm}\) |
\(\large{ a, b, c }\) = edge | \(\large{ in}\) | \(\large{ mm }\) |
Trig Functions |
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Find A
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Find B
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Find a
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Find b
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Find c
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Find Area
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Tags: Triangle