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Height of a scalene triangle

Details
1.  The height of a triangle if you know all sides  

height arbitrary triangle 2

a , b , c    -  sides

s  - semiperimeter    

s F

h  - height  measured at right angle to the base

 

Calculate the height of a triangle if given sides  ( h  ) :

height arbitrary triangle F11

 

 

2.  The height of a triangle if you know side and angle or area and base  

height arbitrary triangle

b , c    - lateral sides

a black  - base

alpha red , beta blue    -  angles at the base

A18 black  - area of a triangle

h  - height  measured at right angle to the base

 

Calculate the height of a triangle if given side and angle at the base  ( h  ) :

height arbitrary triangle F21   height arbitrary triangle F22

 

Calculate the height of a triangle if given area and base  ( h  ) :

height arbitrary triangle F3

 

 

3.  The height of a triangle if you know sides and radius of the circumcircle  

height arbitrary triangle R

b , c    - lateral sides

R14 red  - radius of the circumcircle of a triangle

O black  - circumcenter    

h  - height  measured at right angle to the base

 

Calculate the height of a triangle if given two lateral sides and radius of the circumcircle  ( h  ) :

height arbitrary triangle F4