# Drawing triangles using lengths and angles?

I am just about getting my head around the tikz point grid and have managed to draw triangles using this method, but is there a way I can draw by directly inputing line lengths and angles?

e.g. if I wanted angles of 125 degrees, 40 Degrees and 15 degrees with the Hypotenuse at 15cm, how would I set this out?

• May be try Intersections as explained in Section 13.3.2 of Tikz Manual version 3.0.1a. Or you can tweak the trapezium shape as defined in Section 67.3 of the same manual. Jul 9 '17 at 22:25

Like this?

\documentclass[margin=1cm]{standalone}

\usepackage{tikz}
\usetikzlibrary{intersections}

\begin{document}
\begin{tikzpicture}
\def\angf{40} %First angle
\def\angs{125} %Second angle
\def\hypo{15} %Hypotenus
\coordinate (O) at (0,0);
\draw[name path=line 1] (O) --++ (\angf:\hypo) coordinate (A);
\path[name path=line 2] (O) --++ (0:2\hypo);
\path[name path=line 3] (A) --++ (-\angs:2\hypo);
\path [name intersections={of=line 2 and line 3,by=E}];
\pgfresetboundingbox
\draw (O)--(E)--(A);
\end{tikzpicture}
\end{document} • A \pgfresetboundingbox before \draw (O)--(E)--(A); will reduce the bounding box to the triangle and not include the (too long) paths line 2 and line 3. And as a remark: since the hypotenuse is the longest side of a triangle, a length of just \hypo for these paths would be enough.
– Mike
Jul 9 '17 at 23:28

For comparison, here is an alternative method using Metapost. (The code is ConTeXt code, but you can also use metapost code in LaTeX using the gmp package).

In Metapost, unknown numeric values may be specified using the whatever keyword. Metapost figures out the value of whatevers so that all equations are satisfied.

Let's label the vertices of the triangle as A, B, and C. Suppose we want to draw AB to be parallel to the x-axis, AC to be the hypotenuse, and angle A to be 40, and angle B to be 125. (Angle C will automatically be 15). We can specify this in Metapost as:

numeric angleA, angleB;
angleA := 40;
angleB := 125;

numeric AC;
AC := 15cm;


We choose point A as origin. Then point C is completely specified

pair A, B, C;

A := origin;
C := (AC,0) rotated angleA;


To specify point B, we give two equations for B. First is that B should be AB distance from A along the x-axis, i.e.,

B = (whatever, 0);


Second, that CB should be at an angle B, i.e.,

B = ((whatever,0) rotated -angleB) shifted C;


Metapost figures out a consistent solution for these two specifications. Here is the complete code:

\starttext
\startMPpage[offset=3mm]
begingroup;
numeric angleA, angleB, angleC;
angleA := 40;
angleB := 125;

numeric AC;
AC := 15cm;

pair A, B, C;

A := origin;
C := (AC,0) rotated angleA;

% Let Metapost figure out B.
B = (whatever, 0);
B = ((whatever,0) rotated -angleB) shifted C;

path triangle ;
triangle := A -- B -- C --cycle;

draw triangle;

pair c; c := center triangle;

freedotlabel("$A$", A, c);
freedotlabel("$B$", B, c);
freedotlabel("$C$", C, c);

endgroup;
\stopMPpage
\stoptext


which gives • This is indeed a very nice application of whatever (and nice use of freedotlabel). May I ask why you include the begingroup; and endgroup;? Is it for "good coding style" only? Jul 10 '17 at 5:29
• @mickep: Using beinggroup and endgroup is out of habit. In ConTeXt, all MP drawings are processed using a single metapost instance, which can sometimes create interference across multiple drawings. So, I always use beinggroup and endgroup to keep the definitions local. Jul 10 '17 at 5:48
• Thanks for clarification. I like that all MP drawings are processed in a single instance. That way, one can "borrow" settings/variables from other (earlier) drawings, like boundingboxes. Jul 10 '17 at 5:51
• Nice. Here's one tiny addition. center gives you the center of the bounding box of a path, rather than the centroid of the path. As a quick alternative for a triangle, you could use the point 2/3[A,1/2[B,C]]. In some cases this might give you a better result with freedotlabel. Jul 17 '17 at 11:09

The angle-lengths relations are given by the law of sines.

## The output ## The code

\documentclass[12pt,tikz]{standalone}
\begin{document}
\begin{tikzpicture}[scale=.5]
% "hypothenuse"
\def\A{15}
% the angles
\def\angA{125}
\def\angB{40}
\pgfmathsetmacro{\angC}{180-\angA-\angB}
% the law of sines
\pgfmathsetmacro{\d}{\A/sin(\angA)}
\pgfmathsetmacro{\C}{\d*sin(\angC)}
\draw (0,0) -- (\angB:\A) -- (0:\C) -- cycle;
\end{tikzpicture}
\end{document}