Is there an equation to calculate the length of a triangles sides given only the angles and the length from the tip of the triangle to its base? If so please express the equation using the following variables AX: the angle of side X L: the length from tip to base It seems like it should be possible, right? If I'm mistaken, please correct me and if there is a way to calculate the lengths without being given the lengths please tell me.
Thank you!
Let the three sides be $a,b,c$ (unknown variables) and the opposite angles are $A,B,C$ (known values) then:
$\frac {\sin A}{a} = \frac {\sin B}b = \frac {\sin C}c$ by the law of sines.
Let the altitude for the tip of triangle (the vertex of angle B) to the base ($b$) be $h$ (a known value). By trig definitions:
$h = \frac {\sin A}c = \frac {\sin C}a$.
So ....
do it.....
$a = \frac {\sin C} h$
$c = \frac {\sin A} h$
$b = \frac a{\sin A}\sin B = \frac c{\sin C}\sin B = \frac {h\sin B}{\sin A \sin C}$