How do I find the height of a triangle without the area??

Thanks in advance!!

M

Mathew120 Jan 14, 2015

#1**+5 **

This link might help: http://www.wikihow.com/Find-the-Height-of-a-Triangle

Rampager1998 Jan 14, 2015

#2**0 **

u divide ur answer they gave you by the other amount on the triangle. then divide by 1/2

Guest Jan 14, 2015

#3**+10 **

Best Answer

**How do I find the height of a triangle without the area??**

$$\boxed{h_c=\dfrac{a*b}{c}}$$

heureka Jan 15, 2015

#4**+5 **

**Really Heureka??**

If I had more time I would try and work out how that could be demonstrated.

I did try a little but I had no success.

I don't remember seeing anything like it before.

Can you show me a proof of this?

Melody Jan 15, 2015

#5**+5 **

Assuming you know the length of all three sides you could make use of Heron's formula. If the sides are of length a, b and c, and b is the base then

$$\frac{1}{2}\times b\times h=\sqrt{s(s-a)(s-b)(s-c)}$$

where h is the height and s is the semi-perimeter (=(a+b+c)/2). This can be rearranged to find h.

.

Alan Jan 15, 2015

#6**+5 **

See the question was: Height of a **right** triangle without area :

$$\\(1) \quad Area = \dfrac{h_c*c}{2} \\\\

(2) \quad Area = \dfrac{a*b}{2}\\\\

\dfrac{h_c*c}{2} = \dfrac{a*b}{2} \\\\

h_c*c = a*b \\\\

h_c= \dfrac{a*b}{c} \\\\$$

heureka Jan 15, 2015

#7**+8 **

Thanks Heureka,

Sorry I did not notice that we were talking only of right triangles.

In my defence there is no 'right' in the question it is only in the title.

ALSO note:

The height that is being found here is the perpendicular distance from the hypotenuse to the right angle vertex.

Melody Jan 15, 2015