Geometry/Chapter 4/Lesson 8

Introduction
This short page serves to teach the reader on how to find the altitude of a triangle.

Finding altitude in a right triangle



 * y = Hypothenuse of $$ABD$$
 * x = Altitude
 * z = Hypothenuse of $$ADC$$


 * 1) $$x =$$ $$\tfrac{x}{4}=$$ • $$\tfrac{7}{x}$$
 * 2) $$y =$$ $$\tfrac{y}{4}=$$ • $$\tfrac{11}{y}$$
 * 3) $$z =$$ $$\tfrac{z}{7}=$$ • $$\tfrac{11}{z}$$

Solving for x

 * 1) $$x =$$ $$\tfrac{x}{4}=$$ • $$\tfrac{7}{x}$$
 * 2) √$$x$$2 $$=$$ √$$28$$
 * 3) $$x =$$ $$2$$√$$7$$

Solving for y

 * 1) $$y =$$ $$\tfrac{y}{4}=$$ • $$\tfrac{11}{y}$$
 * 2) √$$y$$2 $$=$$ √$$44$$
 * 3) $$y = 2$$√$$11$$

Solving for z

 * 1) $$z =$$ $$\tfrac{z}{7}=$$ • $$\tfrac{11}{z}$$
 * 2) √$$z$$2 $$=$$ √$$77$$
 * 3) $$z =$$ √$$77$$

Answer:
 * $$x =$$ $$2$$√$$7$$
 * $$y = 2$$√$$11$$
 * $$z =$$ √$$77$$