In triangle ABC, |AC| = 7, |BC| = 5, and |AB| = 8. Find the

[nessabear91]

In triangle ABC, |AC| = 7, |BC| = 5, and |AB| = 8. Find the length of the altitude of the triangle to side AB.

I know about altittudes and that the altitude forms two right triangles. I also know that AB can be two segments with the lengths "x" and "x - 8". But past that point, I get lost. I'm pretty sure I'm supposed to use the Pythagorean Theorom, but I don't know how to apply it to get the answer.

 

[stapel]

Draw the picture of ABC, along with the altitude, so you've formed the two right triangles.

Label the sides, as appropriate, with "7", "5", "x", and "x - 8". Label the height line as "h".

Apply the Pythagorean Theorem to each of the two right triangles. This will give you two equations in two variables.

Solve each equation for "h²=", and set the results equal to each other. You now have one equation in one variable.

Solve the quadratic equation for the value of "x". Then back-solve to find the value of "h".

If you get stuck, please reply showing how far you have gotten in working through the above steps. Thank you.

Eliz.

 

[pka]

Here is a second way.
Use Heron’s formula to find the area of the triangle:
http://mathworld.wolfram.com/HeronsFormula.html .
The find the altitude from the area.