Sam just moved from the UK to Sydney, and has hired a tour Guide to show him to the Sydney Opera House
So how tall is the building then?
This is the Sydney Opera House, the most famous landmark in the city. We are standing 200 meters away from the building, and the angle of elevation from us to the top is 45 degrees
Height of Opera House
Thank You!!
we can work that out with what I just told you, through use of tangent ratio:tan(45) = height / 200200 * tan(45) = heightheight = 200 meters
200 meters
45 degrees
The shape of the Opera House immediately reminded me of an outline of a triangle
Yes that is very commonly mentioned, in actual fact, if a triangle was to be created using the top of the Opera House and each side at the bottom, the dimensions would be 250 meters, 350 meters, and 400 meters
We could find the area of the Opera House in this 2-Dimensional plane as we are observing it from it's highest point and it's widest points. Using Heron's Formula, area is calculated by first finding s, which equals (250+350+400)/2=500. And then finding the difference between s and each side, then multiplying all of these numbers together, and then finding the square root of that result to find the final result. 500(500-250)(500-350)(500-400)=1.875e9. And the square root of this is 43301.27 meters squared.
250 meters
What can I do with this information
400 meters
350 meters
Thank you so much for the tour of the Opera House. I've got to get going now, Bye!
No problems, Bye!
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