Math Report

1. The method our group used to find the measurements of the castle wall were; first the similar or congruent triangle method were from the sketch of the tree and the castle wall we drew trianglesfrom the top of the castle wall to the end of its shadow and from the top of the tree to the end of its shadow. There we found to similar triangles. They are similar because the measurement of theirangles is congruent. The second method was cross-multiplying. In class Mr. Osborn gave us 3 measurements; the first one was height of the tree, which is 4.5m, then the length of the tree shadow that was15m, finally the length of the castle shadow, which is 60m. Look at the two triangles in one you have 4.5m and 15m so you write them as a fraction, besides in the other triangle you see 60 which is inthe same side of the triangle as 15m because both are shadow measurements. In another fraction you put 60m parallel to 15m and parallel to 4.5m you put X. ex. 15m = 60m4.5m = X .
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4. When calculating the height of the wall and calculating the model sizes there was some similarities and somedifferences. The similarities were that because we were passing 1m into 1cm it was easy to calculate because the only thing you had to change was the measuring system. There were no mathematical calculationsneeded. The differences were that in the model the wall was much more smaller than the actual wall.
5. I believe maybe there are other strategies to solve the problem but definitely this is the mostefficient. Maybe with only the cross multiplying you could get the answer but the similar triangles lets you see the similarities between the numbers easier.
6. The grandest mathematical part ofthis project was making everything on the model to scale because generally you just get every thing and past it no matter what the size is and here you actually had to measure how tall everything was...