Question

A rectangular doorway is 38 meters wide and 60 meters high. The doorway is capped with a semi-ellipse that is 13 meters high at its center. Find the height h of the doorway and window 5 meters from the center.

From the ellipse equation, I can see that a should be 19 and b should be 13. From the description in the word problem, it sounds like the top half of an ellipse, so it sounds like a semi ellipse equation should be written x = -square root of the ellipse equation. I'm at a loss to find the equation or to solve the question. Please help! Thank you.

Answer 1

So if you place the ellipse with centre at (0,0), we have
a=19 and b = 13 , and the equation would be
x^2/19^2 + y^2/13^2 = 1
or
x^2/361 + Y62/169 = 1

Now if x = 5
25/361 + y^2/169 = 1
y^2/169 = 336/361
y^2 = 157.296...
y = 12.54

adding on the 60 m it would be 72.54 m high.

Wow, curious where we could find that structure.