Special Right Triangles - its a short cut to find the missing sides of a right triangle.
Some angle combinations are a short cut to find the side length of a triangle easier and quicker. One angle combination is 45 - 45 - 90 where the hypotenuse is across the 90 degree angle and the 45 - 45 angles are across from the 2 congruent sides.
On a 45 - 45 - 90 triangle the Hypotenuse = xradical2 and the two legs are x
the other angle combination is 30 - 60 - 90 where the Hypotenuse is still across from the 90 degree angle. but the sides are not all congruent. The hypotenuse = 2x , The short side = x, The long side = xradical 3.
another combination i have dicroverd is 10 - 80 - 90. it has the same shap as 30 - 60 - 90 but different lengths. i wonder if they can have the same formula but it uses a smaller number.
Short Leg Long Leg Hypotenuse Angle A Angle B Angle C
0 0 0 10 0 80
.2 cm 1 cm 1 cm 10 90 80
.4 cm 2 cm 2 cm 10 90 80
.5 cm 3 cm 3 cm 10 90 80
.7 cm 4 cm 4 cm 10 90 80
.9 cm 5 cm 5 cm 10 90 80
1. cm 6 cm 6 cm 10 90 80
It seems like every whole number equals a multiple of 6. Like if I said that the Short Leg equals 5 the the Hypotenuse and Long Leg equals 30.
My equation is the SL = x, LL = 6x, H = 6x
When you plug these numbers in you will see that this could be another possible Special Right Triangle.
If you start 2cm then go up 6cm every time you get .4cm, 2.4cm, 3.4cm, 4.4cm.
You have to start at the Hypotenuse.
What can you say about the 10-80-90 triangle? Have you researched what the side lengths are for different versions of this triangle? Can you share some of your data? Can you find any patterns in your data?
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