triangle pattern 10-90-80

Since the last time I blogged, I had discovered a pattern in a 40-60-80 Triangle. Now I am working with a Right Triangle, 10-90-80. I have discovered a pattern in the relationship between the side lengths.

The angle combination that shows a similar pattern is the 10-90-80 Triangle. There is a relationship between the Longer Leg and the Short Leg and between the Longer Leg and the Hypotenuse Leg. The relationship between the Longer Leg and the Short Leg is the Longer Leg x .1763 = Short Leg. This relationship is shown in the table below. There is another relationship between the Longer Leg and the Hypotenuse Leg. The relationship is Longer Leg x 1.0154 = Hypotenuse Leg. This relationship is shown in the table below.

Longer Leg	1	2	4	5	6	7	8	9	10
Short Leg	0.1763	0.3526	0.5289	0.7053	0.8816	1.0579	1.2342	1.4106	1.5869	1.7632
Hypotenuse Leg	1.0154	2.0308	3.0462	4.0617	5.0771	6.0925	7.1079	8.1234	9.1388	10.1542

I had to take many steps to investigate this triangle. I used the website: http://www.saltire.com/applets/triangles/tri1s2a.htm to find my information. It also took me some complicated calculations to get this pattern. My next step will be to finish looking at all Right Triangles and seeing if they have a similar pattern to eachother.

A Different Triangle Pattern

We have discovered that there are patterns that appear in the lengths of right triangles with the angles 30-60-90 and with the angles 45-45-90. Are there any other angle combinations that show similar patterns?

The angle combination that shows a similar pattern is the 80-60-40 Triangle. There is a relationship between the Short Leg and the Hypotenuse Leg and between the Short Leg and the Longer Leg. The relationship between the Short Leg and the Hypotenuse Leg is the Short Leg x 1.532 = Hypotenuse Leg. This relationship is shown in the table below. There is another relationship between the Short Leg and the Longer Leg. The relationship is Short Leg x 1.347 = Longer Leg. This relationship is shown in the table below.

Short Leg	1	2	3	4	5	6	7	8	9	10
Hypotenuse Leg	1.532	3.065	4.597	6.129	7.661	9.193	10.725	12.257	13.789	15.321
Longer Leg	1.347	2.694	4.041	5.389	6.736	8.083	9.431	10.778	12.125	13.472

I had to take many steps to investigate this triangle. I used the website: http://www.saltire.com/applets/triangles/tri1s2a.htm to find my information. It also took me some complicated calculations to get this pattern.

We have discovered that there are patterns that appear in the lengths of right triangles with the angles 30-60-90 and with the angles 45-45-90. Are there any other angle combinations that show similar patterns?