## 02ps-15 Height Of The Duomo Solution

• 0:00 - 0:04
To solve this problem, the first thing I did was say, okay, well,
• 0:04 - 0:08
it looks like this is directly in the middle of this building--this spire.
• 0:08 - 0:12
I can draw some imaginary line, making this distance 25 m.
• 0:12 - 0:15
Now, you could have used trigonometry to solve this question.
• 0:15 - 0:17
But there was a trick.
• 0:17 - 0:21
You could have solved it in a slightly easier way by using similar triangles.
• 0:21 - 0:23
To use the similar triangle method,
• 0:23 - 0:27
we notice that this triangle in purple is similar to this triangle in green.
• 0:27 - 0:29
Now, what are the dimensions of this green triangle?
• 0:29 - 0:33
Well, at 60 m along the base from here, and 15 meters here--
• 0:33 - 0:36
simply because this height is 60,
• 0:36 - 0:39
and we subtract the 45. What about the purple triangle?
• 0:39 - 0:45
Well, the base is 180 m--60 + 35 + 60 plus this 25.
• 0:45 - 0:47
The height is unknown.
• 0:47 - 0:51
This is what we're solving for. I'm going to erase our man to give ourselves some room.
• 0:51 - 0:53
We can set up a ratio.
• 0:53 - 0:56
The ratio of this side to that side must be the same as x to 180.
• 0:56 - 0:58
We multiply both sides by 180 to solve for x.
• 0:58 - 1:02
When we do out the arithmetic, we find x = 45 m,
• 1:02 - 1:06
but we also have to add in the original 45 m to get the full height of the Duomo.
• 1:06 -
The answer is that the height of the Duomo is 90 m. Very good work.
Title:
02ps-15 Height Of The Duomo Solution
Video Language:
English
Team:
Udacity
Project:
PH100 - Intro to Physics
Duration:
01:11