Question

"The hypotenuse of right triangle is 2 units longer than its height. Determine a formula for the height as a function of the base b.

Answer 1

Have you tried drawing a picture of the triangle and its lengths?

Answer 2

So far I have h^2 + b^2 = (h+2)^2

Answer 3

\[h = \sqrt{c^{2} - b^{2}},\], where c = h + 2 is the hypotenuse. Then
\[h = \sqrt{(h + 2)^{2} - b^{2}}\]
\[h^{2} = h^{2}+ 4h + 4 - b^{2}\]\[4h = b^{2} - 4\]
\[h = (b^{2} - 4)/4.\]

Answer 4

Oh! I see. I was solving for the wrong variable. Thanks!

Answer 5

:^)