The height of the given object is 35 feet tall.
From the given parameters:
The two legs of the right triangle = x and (x - 85)
The hypotenuse side, = 125
The length of the shadow is calculated by applying Pythagoras theorem as follows;
[tex]x ^2 + (x - 85)^2 = 125^2\\\\x^2 + x^2 -170x + 7225= 15625\\\\2x^2 - 170x -8,400 = 0\\\\2(x^2 -85x - 4,200) = 0\\\\x^2 -85x - 4,200 = 0\\\\[/tex]
Factorize the equation as follows;
[tex]x^2 + (35x - 120x) - 4200= 0\\\\x^2 + 35x \ - 120 x - 4200 = 0\\\\x(x + 35) - 120(x + 35) = 0\\\\(x + 35) (x -120) = 0\\\\x = - 35 \ \ or \ 120\\\\[/tex]
The length is always positive, thus, x = 120 ft
The height of the object is calculated as follows;
h = x - 85
h = 120 - 85
h = 35 ft
Thus, the height of the given object is 35 feet tall.
Learn more about Pythagoras theorem here: https://brainly.com/question/12306722
