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January 9, 2019

Grade 10s are working with similar triangles and trigonometry. 

We started with a 90 degree angle and the sides 10cm and 9cm in one triangle, and 27cm and 30cm in the other.  Using our knowledge of the pythagorean theorem we calculated the hypotenuse.  We also used our learning from Monday to calculate the value of the angles using our trig tables.  We had the option to use the ratio for sine, cosine or tangent since we knew all 3 sides.  

We noticed that the angles are the same in both triangles, and the side lengths are proportional.  This is always the case!  We have 2 similar triangles.  We also looked at the areas and compare them.  Our big triangle has sides that are 3 times the length of the small triangle sides.  The are of the big triangle is 9 times the area of the small one. Thats 3^2 (three squared).  This relationship holds true for similar triangles.  If the proportionality constant is “k” between the sides of the triangle, it will mean that the areas have a proportionality constant of “k^2”.

We looked at a situation where we can use similar triangles.

We can determine the height of an object by using shadows.  

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