SOLUTION: Hello! I need help with this triangle problem. Thanks! The sides of a right triangle are 6, 8, and 10. Find the altitude drawn to the hypotenuse.

Algebra ->  Triangles -> SOLUTION: Hello! I need help with this triangle problem. Thanks! The sides of a right triangle are 6, 8, and 10. Find the altitude drawn to the hypotenuse.       Log On


   

Question 771064: Hello! I need help with this triangle problem. Thanks!
The sides of a right triangle are 6, 8, and 10. Find the altitude drawn to the hypotenuse.
Found 2 solutions by josmiceli, MathLover1:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
This is a 3-4-5 with each side multiplied by +2+
Let +h+ = altitude
The altitude divides the 10-side into +c+ and
+10+-+c+
------------
The two right triangles formed have sides
+c+, +h+, and +6+
also
+10-c+, +h+, and +8+
--------------------------
+c%5E2+%2B+h%5E2+=+6%5E2+
and
+%28+10-c+%29%5E2+%2B+h%5E2+=+8%5E2+
-------------------------
Eliminate +c+ and solve for +h+
I have to run

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
here is what we use to solve this problem:
The Pythagorean Theorem:
c%5E2+=+a%5E2+%2B+b%5E2



given:
a=+6, b=8, and c=10
If an altitude is drawn to the hypotenuse of a right triangle, then each leg is the geometric mean between the hypotenuse and its touching segment on the hypotenuse.
by this theorem, c%2Fa=a%2Fx and c%2Fb=b%2Fy
first find x and y:
+c%2Fa=a%2Fx
+10%2F6=6%2Fx
+10x=36
x=36%2F10
x=3.6
c%2Fb=b%2Fy
10%2F8=8%2Fy
10y=64
y=6.4

then the altitude h%5E2=a%5E2-x%5E2
h%5E2=6%5E2-3.6%5E2
h%5E2=36-12.96
h%5E2=23.04
h=4.8
or
h%5E2=b%5E2-y%5E2
h%5E2=8%5E2-6.4%5E2
h%5E2=64-40.96
h%5E2=23.04
h=4.8