# 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
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