#### Answer

By what we learned in this section, and by using the pythagorean theorem we could find the altitude.
Step 1 : let “ b “ be the altitude, and since b separates the hypotenuse into two unequal parts, let’s name one as “ x” and the second as “ y “ for facility.
Step 2 : b separates the original triangle into two similar triangles with legs 6 and 8 inches and the hypotenuse is 10 in.
Step 3 : apply pythagorean theorem in triangle 1
$ 6^{2}=b^{2} + x^{2} $, and apply the same theorem in the second triangle therefore
$ 8^{2}= b^{2}+ y^{2} $.
Step 4 : since x + y = 10 then x= 10-y.
Substitute x in the step two and evaluate it . We obtain
$ 36= b^{2}+ 10^{2}-20y+y^{2} $.
$ y^{2}+ b^{2}+64-20y = 0 $.
Step 4 : create a system of equation between
$ y^{2}+ b^{2}+64-20y = 0 $
$ b^{2}+ y^{2} - 64=0 $
Step 5 : by subtraction we conclude 128-20y=0
Therefore y= 6.4
Step 6: by substituting y in one of the equations in Step 4 we obtain that b= height= 4.8.

#### Work Step by Step

I used the equation for altitude to find this value.