Right Triangle Formulas

Posted In: Mathematics

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.

Right Triangle

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

  1. $α+β=90°$
  2. $sin\ α=a/c=cos\ $β
  3. $cos\ α=b/c=sin\ $β
  4. $tan\ α=a/b=cot\ $β
  5. $cot\ α=b/a=tan\ $β
  6. $sec\ α=c/b=cosec\ $β
  7. $cosec\ α=c/a=sec\ $β
  8. Pythagorean Theorem
    $a^2+b^2=c^2$
  9. $a^2=fc, b^2=gc$,
    where f and c are projections of the legs a and b, respectively, onto the hypotenuse c.
  10. $h^2=fg$,
    where h is teh altitude from the right angle.
  11. $m_a^2+b^2-{a^2}/4, m_b^2=a^2-{b^2}/4$,
    where m_a and m_b are the medians to the legs a and b.
  12. $m_c=c/2$,
    where m_c is the median to the hypotenuse c.
  13. $R=c/2=m_c$
  14. $r={a+b-c}/2={ab}/{a+b+c}$
  15. $ab=ch$
  16. $S={ab}/2={ch}/2$

Post Tags: Geometry


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