I'm not sure if this is the easiest way of doing this, but it surely work.
Let the base of the triangle be AB, and let CH be the height. Just for reference, we have

Moreover, let CH=y and BC=z
Now, AHC, CHB and ABC are all right triangles. If we write the pythagorean theorem for each of them, we have the following system

If we solve the first two equations for y squared, we have

And we can deduce

So that the third equation becomes

(we can't accept the negative root because negative lengths make no sense)
Sorry my hand writing isn’t the best but here is the work for it and the answer would be (228in)
Answer:
We are given:

is the critical value at 0.02 significance level
is the margin of error
Therefore, the required sample size is:




Therefore, the required sample size n = 1061
Multiply both sides of the equation by 28 4y+7=10
Then move constants to the right side and change its sign 4y=10-7
Now subtract the numbers 4y=3 divide both sides by 4 so your answer is y=3/4
No the triangle is not a right triangle