Question

How to find the height of a triangle without area?

Answer 1

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explanation
The height of a triangle is the length of the line segment that runs from a vertex of the triangle to the side opposite that vertex and is perpendicular to the side opposite the vertex.

We have a nice formula that relates the sides of a right triangle called the Pythagorean Theorem. It says that if a right triangle has side lengths a , b, and
c , where c is the longest side (called the hypotenuse), then the following equation is true:
a 2 + b2 = c 2

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Answer 2

A triangle holds three sides and when their measurements are provided, then its height can be determined, as follows.

First of all we have to find its semi-perimeter S,  

S =$\frac{a + b + c}{2}$  

Then with that, lets find the area of the triangle.

Area = $\sqrt{(s(s-a)(s-b)(s-c))}$

Having its measurements of the area, we can determine its height.

Area = $\frac12(bh)$  

h =$\frac{2 * Area}b$  

h – height of the triangle

b – base of the triangle

When only two of its sides and an angle being given, then finding the height of the triangle is followed as,

Area =$\frac12$(ab sin C)  

Area =$\frac12$(bh)  

So we can write

$\frac12(bh)=\frac12(ab\ sin\ C)$  

$h =\frac{ab (sin C)}b$