Three altitudes

A triangle with altitudes 4, 5, and 6 cm is given. Calculate the lengths of all medians and all sides in a triangle.

Correct answer:

a =  7.5236 cm
b =  6.0189 cm
c =  5.0157 cm
t1 =  4.0671 cm
t2 =  5.6413 cm
t3 =  6.3345 cm

Step-by-step explanation:

v1=4 cm v2=5 cm v3=6 cm  h=21/v1+1/v2+1/v3=21/4+1/5+1/6=120370.3083 t=h (h1/v1) (h1/v2) (h1/v3)=12037 (120371/4) (120371/5) (120371/6)0.0003  s=4 t=4 0.00030.0665 S=s1=0.0665115.0472 cm2  S = 2a   v1  a=2 S/v1=2 01/4=7.5236 cm

Try calculation via our triangle calculator.

b=v22 S=52 01=6.0189 cm
c=v32 S=62 01=5.0157 cm
t1=22 b2+2 c2a2=22 6.01892+2 5.015727.52362=4.0671 cm
t2=22 a2+2 c2b2=22 7.52362+2 5.015726.01892=5.6413 cm
t3=22 a2+2 b2c2=22 7.52362+2 6.018925.01572=6.3345 cm



Did you find an error or inaccuracy? Feel free to write us. Thank you!







Tips for related online calculators
Looking for calculator of harmonic mean?
Looking for a statistical calculator?
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
Do you want to convert length units?
The Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:


 
We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions: