Triangles & trigonometry

1. Universal triangle solver (SSS, SAS, ASA, AAS, SSA)
2. Triangle altitudes from three sides
3. Right triangle & Pythagorean solver
4. Special right triangles (30-60-90, 45-45-90)
5. All six trigonometric & inverse functions
6. Angular size & distance

$$c^2=a^2+b^2-2ab\cos C,\quad \frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C},\quad \text{Area}=\sqrt{s(s-a)(s-b)(s-c)}$$

Law of Cosines + Law of Sines + Heron's formula. Sides are $a,b,c$; the angle opposite each side is $A,B,C$. SSA may yield two triangles. Source: 1728 Software Systems.

$$h_a=\frac{2\,\text{Area}}{a},\quad h_b=\frac{2\,\text{Area}}{b},\quad h_c=\frac{2\,\text{Area}}{c}$$

Each altitude is the perpendicular distance from a vertex to the opposite side. Area from Heron's formula. Source: 1728 Software Systems.

$$c=\sqrt{a^2+b^2},\quad A=\arctan\frac{a}{b},\quad \sin A=\frac{a}{c},\ \cos A=\frac{b}{c}$$

Legs $a,b$; hypotenuse $c$; angle $A$ opposite leg $a$. Enter the two known legs. Source: 1728 Software Systems.

$$45^\circ\text{-}45^\circ\text{-}90^\circ:\ x:x:x\sqrt2,\qquad 30^\circ\text{-}60^\circ\text{-}90^\circ:\ x:x\sqrt3:2x$$

Exact radical side ratios from one known reference side $x$ (the short leg). Source: 1728 Software Systems.

$$\csc\theta=\frac1{\sin\theta},\quad \sec\theta=\frac1{\cos\theta},\quad \cot\theta=\frac1{\tan\theta}$$

All six functions for an angle in degrees, radians, or gradians (400 grad = 360°). Source: 1728 Software Systems.

$$\theta=2\arctan\!\left(\frac{g}{2d}\right)$$

Relates physical size $g$, viewing distance $d$, and apparent angular size $\theta$. Provide any two; the third is solved. Source: 1728 Software Systems.