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December 1st, 2018, 05:33 AM   #1
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The inverse of one angle and the side opposite to the angle, which is equal to one, in all triangles gives a diameter of the circumscribed circle.

In a right triangle, the inverse of the angle is always 1, which is the circle's diameter, and its opposite's side is 1, that is hypotenuse of 1. $\sin 90 =1$ is the angle $\theta$.


My question is, what is the right explanation concerning the inverse of angles with sides $a,b,c$ for all $\triangle ABC$ when the base or the hypotenuse equals to 1?

1) explanation

I have three sides $5, 5, 4$ and $1.25, 1.25, 1$ with all the same angles except the base is 1, and all I did is divide sides $5, 5, 4$ by 4 to obtain the simplified version of the triangle sides. $1.25, 1.25, 1$. From the $\triangle ABC $ and 1, the side $c$ opposite to the $\angle C =\sqrt {1-0.68^2}$. Its inverse is the diameter of circumscribed circle in terms of $\sin$, but not in terms of cosine.

The law of sines states that:

$$\frac {\sin A}{a}=\frac {\sin B}{b}=\frac {\sin C}{c}=\frac {1}{d}$$ where d is the diameter.

$$\frac {a}{\sin A}=\frac {b}{\sin B}=\frac {c}{\sin C}={d}$$ where d is the diameter.

Last edited by skipjack; December 1st, 2018 at 09:52 AM.
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