Answer:
Step-by-step explanation:
Set up the Pythagorean Equation for the two triangles
x^2 + h^2 = 4^2 = 16
(x + 6)^2 + h^2 = 8^2 = 64
x^2 + h^2 = 16 Subtract. That will get rid of h^2
(x + 6)^2 - x^2 = 64 - 16 Expand the brackets. combine the right.
x^2 + 12x+36 - x^2 = 48 Combine
12x + 36 = 48 Subtract 36 from both sides
12x +36 -36 = 48-36 Combine
12x = 12 Divide by 12
12x/12 = 12/12
x = 1
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x^2 + h^2 = 4^2
1^2 + h^2 = 16
h^2 = 15
h = sqrt(15)
