SOLUTION: A window has the shape of a square of side length 60 cm surmounted by a segment of a circle of radius 50 cm. The circle segment is less than a semicircle. What is the maximum heigh

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Question 1195528: A window has the shape of a square of side length 60 cm surmounted by a segment of a circle of radius 50 cm. The circle segment is less than a semicircle. What is the maximum height, in centimetres, of the window?
Answer by ikleyn(52781) About Me  (Show Source):
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A window has the shape of a square of side length 60 cm surmounted
by a segment of a circle of radius 50 cm. The circle segment is less
than a semicircle. What is the maximum height, in centimeters, of the window?
~~~~~~~~~~~~~~ 

Make a sketch on your own.


In the sketch, the center of the circle is somewhere inside the square.

Connect the center with the square's upper corners by straight lines.

Draw a perpendicular from the center to the mid-point of the upper horizontal
side of the square.


In the sketch, you have a right-angled triangle.
Its hypotenuse is 50 cm. One of its leg (horizontal) is 60/2 = 30 cm long.


Hence, according to the Pythagorean theorem, its other leg (vertical) has
the length of  sqrt%2850%5E2-30%5E2%29 = 40 cm.


It means that the maximum height of the window is 60 cm + 60 cm + (50-40) cm = 130 cm.


ANSWER.  The maximum height of the window is 130 centimeters.

Solved.