00:01
So we have our elliptical arch here that is under a bridge, and it is 60 feet wide.
00:08
So from here all the way to there is 60 feet.
00:14
And at its maximum height, it is 25 feet.
00:17
So from here to there is 25 feet.
00:22
We need to find the height of the arch when it is 15 feet from the center.
00:29
In order to do that, we first need to find an equation for this arch.
00:32
That'll help us find the height at a certain distance from the center.
00:36
So because this arch is oriented horizontally, it's greater in the left and right direction than the top and bottom direction, we will be using the equation x squared over a squared plus y squared over b squared is equal to 1.
00:55
So if we can find the a and the b, then we'll replace those in the equation and we'll have an equation to use.
01:01
So a is the distance that the center is all the way out to the vertex there.
01:08
So if the whole distance here is 60, then that distance would be 30.
01:13
So 30 feet for that distance, and that would be a.
01:20
So a is 30.
01:23
And then b is in the opposite direction.
01:25
It's from the center out to that edge.
01:28
We don't have to cut the 25 and half like we did the 60, because it's not this whole length all the way down there because it's an arch, so it would be a semi -ellipse here.
01:41
So we just need to take b as 25 because it's the distance away from the center to the other edge of the ellipse...