A right triangle or right-angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle). The relation between the sides and angles of a right triangle is the basis for trigonometry.

Legs of a right triangle: a,b

Hypotenuse: c

Altitude: h

Medians: ma,mb,mc

Angles: α,β

Radius of circumscribed: R

Radius of inscribed circle: r

Area: S

- $α+β=90°$
- $sin\ α=a/c=cos\ $β
- $cos\ α=b/c=sin\ $β
- $tan\ α=a/b=cot\ $β
- $cot\ α=b/a=tan\ $β
- $sec\ α=c/b=cosec\ $β
- $cosec\ α=c/a=sec\ $β
- Pythagorean Theorem

$a^2+b^2=c^2$ - $a^2=fc, b^2=gc$,

where f and c are projections of the legs a and b, respectively, onto the hypotenuse c.

- $h^2=fg$,

where h is teh altitude from the right angle. - $m_a^2+b^2-{a^2}/4, m_b^2=a^2-{b^2}/4$,

where m_a and m_b are the medians to the legs a and b.

- $m_c=c/2$,

where m_c is the median to the hypotenuse c. - $R=c/2=m_c$
- $r={a+b-c}/2={ab}/{a+b+c}$
- $ab=ch$
- $S={ab}/2={ch}/2$

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