Answer
By using the same process that we used in excercise 30 which is applying the pythagorean theorem in each small triangle then create a system of equation.
We obtain two pythagorean equations :
$ 10^{2} = ( y-26 )^{2}+ h^{2} $
$ 24^{2}=y^{2}+h^{2} $
Therefore $ y= \frac{120}{13} $
By substituting $y$ in one of the equation above
Then the $ h= \frac{288}{13}\approx 9.2 $
Work Step by Step
I used the equation for altitude, as well as a rough sketch to keep track of the location of the triangle's values, to obtain my solution.
