SOLUTION: How do I find the height of an scalene triangle, where not angle degrees are provided, only the following side dimensions?: The base=21, the longest side=20 and the shortest sid

Click here to see ALL problems on Triangles

Question 9649: How do I find the height of an scalene triangle, where not angle degrees are provided, only the following side dimensions?:
The base=21, the longest side=20 and the shortest side=13
My main problem is that there are no angle degrees information provided.
Thanks in advance for your help.

Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
Try this:
As you know, the height of a triangle is the perpendicular distance to the base from the vertex opposite the base.
Draw the triangle with the base (21) on the bottom. Draw the perpendicular line from the vertex opposite the base to the base.
The scalene triangle is now divided into two right triangles.
The smaller right triangle has a hypotenuse of 13, a height of h, and a base of x.
The larger right triangle has a hypotenuse of 20, a height of h, and a base of 21-x.
Now you can employ the Pythagoren theorem to find h.
Take the smaller right triangle first: or =
Now take the larger right triangle:

Now substitute for h^2 the equation from the 1st right triangle:

Simplify and solve for x.

Now that you have x, you can find h, again using the Pythagorean theorem.
Using the smaller triangle: