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# MCR-3U Trigonometric Ratios

Trigonometric ratios, they are used to measure lengths and angles with even using a calculator or a ruler. Well how can they be used? Lets say you want to measure a building but it's too dangerous to go close to the building so we can use special triangles to determine the height of the building. We can use the 45-45-90 special triangle, we can fold a piece of paper until we get a right-angle triangle and back away from the building until we see the tip of the building with our paper. Now we know that we are looking at the building at a 45 degree angle, so our distance to the building is 1 unit, and the height of the building from the point of the view from the paper if 1 unit. We can't exactly find the exact units of the building due to not given any measurements however if we knew that our distance from the building was 40m then we can determine that your height plus 40m would be the height of the building. Another way we can use trigonometric ratios in real life, is to use 3-4-5 it's exactly the Pythagorean theorem construction workers use this to determine if the corner of a wall is 90 degrees, because they would want that to make the room look sharp and clean so what they would so is they would measure one side 3 m then the other side 4m if the corner was 90 degrees then it would be 5m when we use a ruler to connect those things here is a picture.

With this information construction workers can make rooms look great to potential buyers because they don't want corners that look rushed or unprofessional.

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