Properties Of Triangles — Chapter Summary

In any triangle ABC

In any triangle ABC, the ratio of a side to the sine of its opposite angle is constant and equal to twice the circumradius: $$\frac{a}{\sin A} = \frac

The square of any side

The square of any side of a triangle equals the sum of squares of the other two sides minus twice their product times the cosine of the included angle

Each side of a triangle can

Each side of a triangle can be expressed as the sum of the projections of the other two sides on it: $$a = b\cos C + c\cos B$$ Similar expressions hol

Using the semi

Using the semi-perimeter $s = \frac{a+b+c}{2}$, we can find trigonometric ratios of half-angles: $$\sin\frac{A}{2} = \sqrt{\frac{(s-b)(s-c)}{bc}},\qua

The area $\Delta$ of a triangle

The area $\Delta$ of a triangle can be calculated using Heron’s formula: $$\Delta = \sqrt{s(s-a)(s-b)(s-c)}$$ Alternatively, using trigonometry: $$\De