Facts off triangles when base=1

Trigonometry equalities, inequalities and expressions - sin, cos, tan, cot

Facts off triangles when base=1

Postby Guest » Tue Jan 01, 2019 2:12 pm

I have three measures of three altitudes $h_0,h_1,h_2$ where sides $a,b,c$ are the constant lengths of all triangles and base $c=1$ and $h_0$ is situated on base $c$.
$\frac{h_0}{h_1}=b$,$\frac{h_0}{h_2}=a$ and $ h_1=\sin A$ as well $h_2=\sin B$.

$\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}=\frac{1}{d}$

d=diameter

$\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}=\frac{1}{d}$ if I mutiply by d ,the diameter, it will give an answer of 1, and 1 is the base. And if I multiply the base times 4, all of 3 sides are multiple of 4 including the altitudes. d=diameter

$\frac{a}{\sin C}=\frac{b}{\sin B}=\frac{c}{\sin C}=d$

$\frac{a}{\sin⁡ A}=\frac{b}{\sin ⁡B}=\frac{c}{\sin ⁡C}=d$
Guest
 

Re: Facts off triangles when base=1

Postby HallsofIvy » Tue Mar 12, 2019 8:30 am

"d= diameter". Diameter of what circle? I would guess either the circumcircle, through the three vertices, or the incircle, tangent to the three sides, but I have no idea which of those.

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