Oblique Triangle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

acute triangleOblique & Acute Triangleobtuse triangleOblique & Obtuse Triangle

 

 

 

 

 

 

 

 

 

 

  • An "oblique" triangle is any triangle that is not a right triangle.
  • An "acute" triangle is when all three angles of the triangle are less than right angles.
  • An "obtuse" triangle is when one of the three angles is greater than a right angle.
  • 3 edges
  • 3 vertexs
  • For "s" and "p" , see semiperimeter

Edge formula

\(a = P - b - c   \)

\(a = 2 \frac {A} {b\;\sin y} \)

\(b = P - a - c   \)

\(b = 2 \frac {A}{h} \)

\(c = P - a - b   \)

Where:

\(a\) = edge

\(b\) = edge

\(c\) = edge

\(P\) = perimeter

\(A\) = area

Height formula

\(h = 2 \frac {A}{b} \)

Where:

\(h\) = height

\(b\) = edge

\(A\) = area

Perimeter formula

\(P = a + b + c \)

Where:

\(P\) = perimeter

\(a\) = edge

\(b\) = edge

\(c\) = edge

Area formula

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

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

Where:

\(A\) = area

\(b\) = edge

Trig Function

  • Find p
    • given a b c: \(\; p= a+b+c \)
  • Find s
    • given a b c: \(\; s= (a+b+c) \div 2 \)
  • Find d
    • given a b c s: \(\; d= (b^2+c^2-a^2) \div 2b \)
  • Find e
    • given a b c s: \(\; e= (a^2+b^2-c^2) \div 2b \)
  • Find h
    • given c A: \(\; h= c*sinA \)
    • given a C: \(\; h= a*sinC \)
  • Find Area
    • given a b c: \(\; Area=\frac {1}{2}(bh) \)
    • given a b c: \(\; Area= sqrt[s(s-a)(s-b)(s-c)] \)
    • given C a b: \(\; Area= \frac{1}{2} ab* \sin c \)
  • Find A
    • given a b c s: \(\; \sin \frac{1}{2} A= sqrt[(s-b)(s-c) \div bc] \)
    • given a b c s: \(\; \cos \frac{1}{2} A= sqrt[s(s-a) \div bc] \)
    • given a b c s: \(\; \tan \frac{1}{2} A= sqrt[(s-b)(s-c) \div s(s-a)] \)
    • given c h: \(\;\ sin A= \frac {h}{c} \)
    • given B a b: \(\;\ sin A= a* sin B\div b \)
    • given B a c: \(\; A= \frac{1}{2}(A+C)+\frac{1}{2}(A-C) \)
    • given C a b: \(\; A= \frac{1}{2}(A+B)+\frac{1}{2}(A-B) \)
    • given C a c: \(\;\ sin A= a* sin C \div c \)
  • Find B
    • given a b c s: \(\; \sin \frac{1}{2} B= sqrt[(s-a)(s-c) \div ac] \)
    • given a b c s: \(\; \cos \frac{1}{2} B= sqrt[s(s-b) \div ac] \)
    • given a b c s: \(\; \tan \frac{1}{2} B= sqrt[(s-a)(s-c) \div s(s-b)] \)
    • given a h: \(\;\ sin B= \frac {h}{a} \)
    • given A a b: \(\;\ sin B= b* sin A \div a \)
    • given A b c: \(\;\ B= \frac{1}{2}(B+C)+\frac{1}{2}(B-C) \)
    • given C a b: \(\; B= \frac{1}{2}(A+B)-\frac{1}{2}(A-B) \)
    • given C a c: \(\;\ sin B= b* sin C \div c \)
  • Find C
    • given a b c s: \(\; \sin \frac{1}{2} C= sqrt[(s-a)(s-b) \div ab] \)
    • given a b c s: \(\; \cos \frac{1}{2} C= sqrt[s(s-c) \div ab] \)
    • given a b c s: \(\; \tan \frac{1}{2} C= sqrt[(s-a)(s-b) \div s(s-c)] \)
    • given A a c: \(\;\ sin C= c* sin A \div a \)
    • given A b c: \(\; C= \frac{1}{2}(B+C)-\frac{1}{2}(B-C) \)
    • given B a c: \(\; C= \frac{1}{2}(A+C)-\frac{1}{2}(A-C) \)
    • given B b c: \(\;\ sin C= c* sin B \div c \)
  • Find a
    • given A B b: \(\; a= b* \sin A \div \sin B \)
    • given A B c: \(\; a= c* \sin A \div \sin (A+B) \)
    • given A C b: \(\; a= b* \sin A \div \sin (A+C) \)
    • given A C c: \(\; a= c* \sin A \div \sin C \)
    • given B C b: \(\; a= b* \sin (A+C) \div \sin B \)
    • given B C c: \(\; a= c* \sin (A+C) \div \sin C \)
    • given A b c: \(\; a= sqrt(b^2+c^2-2bc * \cos A) \)
  • Find b
    • given A B a: \(\; b= a* \sin B \div \sin A \)
    • given A B c: \(\; b= c* \sin B \div \sin (A+B) \)
    • given A C a: \(\; b= a* \sin (A+C) \div \sin A \)
    • given A C c: \(\; b= c* \sin (A+C) \div \sin C \)
    • given B C a: \(\; b= a* \sin B \div \sin (B+C) \)
    • given B C c: \(\; b= c* \sin B \div \sin C \)
    • given B a c: \(\; b= sqrt(a^2+c^2-2ac * \cos B) \)
  • Find c
    • given A B a: \(\; c= a* \sin (A+B) \div \sin A \)
    • given A B b: \(\; c= b* \sin (A+B) \div \sin B \)
    • given A C a: \(\; c= a* \sin C \div \sin A \)
    • given A C b: \(\; c= b* \sin C \div \sin (A+C) \)
    • given B C a: \(\; c= a* \sin C \div \sin (B+C) \)
    • given B C b: \(\; c= b* \sin C \div \sin B \)
    • given C a b: \(\; c= sqrt(a^2+b^2-2ab * \cos C) \)