Right Triangle

Written by Jerry Ratzlaff. Posted in Plane Geometry

right triangle

  • One side of a right triangle is 90 °.
  • The other two angles are unequal and no sides are equal.
  • The hypotenuse of a right triangle is the longest side or the side opposite the right angle.
  • 3 edges
  • 3 vertexs
  • \(a\) = opposite leg
  • \(b\) = adjacent leg
  • \(c\) = hypotenuse

Edge formula

\(a = \sqrt {c^2 - b^2 } \)

\(a = 2 \frac {A} {b}   \)

\(b = \sqrt {c^2 - a^2 } \)

\(b = 2 \frac {A} {a}   \)

\(c = \sqrt {a^2 + b^2 } \)

Where:

\(a\) = edge

\(b\) = edge

\(c\) = edge

\(A\) = area

Perimeter formula

\(P = a + b + c \)

\(P = a + b + \sqrt {a^2 + b^2 } \)

Where:

\(P\) = perimeter

\(a\) = edge

\(b\) = edge

\(c\) = edge

Area formula

\(A= \frac {ab} {2} \)

Where:

\(A\) = area

\(a\) = edge

\(b\) = edge

Trig Function

  • 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: \(\; Area= ab \div2 \)