Oblique Triangle

Written by Jerry Ratzlaff. Posted in Plane Geometry

Oblique & Acute 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: $$\; c= sqrt(a^2+b^2-2ab * \cos C)$$