Geometry, Special Right Triangles

[mbwngnpryr]

I have two problems I can't figure out. One is a 45-45-90 triangle with a hypotenuse of 8, so that 8= n root 2. The other is a 30-60-90 triangle with the longer side length being 8 -- so that 8=n root 3. I know the ratios for the special triangles, but can't figure out how to solve for the sides of these two triangles.

 

[tkhunny]

You just did. What do you mean "solve"? Is there a particular problem statemetn that troubles you?

RBGTHGANH

 

[mbwngnpryr]

I need to find the length of the other two sides -- n and 2n, and I don't know how to take 8=n root 3 and translate it to n and 2n. It should be an algebraic solution, but I can't figure it out -- I am not very good with radicals.

 

[tkhunny]

I am not very good with radicals.

Never say that again. Practice, instead.


I have two problems I can't figure out. One is a 45-45-90 triangle with a hypotenuse of 8, so that 8= n root 2. The other is a 30-60-90 triangle with the longer side length being 8 -- so that 8=n root 3. I know the ratios for the special triangles, but can't figure out how to solve for the sides of these two triangles.

45-45-90 right triangles are ALWAYS \(\displaystyle Hypotenuse = \sqrt{2}\cdot (Side)\). This translatees nicely to \(\displaystyle \frac{Hypotenuse}{\sqrt{2}}\;=\;Side\)

How are you struggling with that? \(\displaystyle Side = \frac{8}{\sqrt{2}}\) Done! Does there need to be more?

 

[mbwngnpryr]

Okay, that makes sense for the 45-45-90 triangle, I think; I need to look at it a little more, because I am still trying to learn what a radical solution should look like.

For the 30-60-90 triangle, would the shorter side, which is n, then be 8 divided by root 3? Making the hypotenuse 2 times (8 divided by root 3)? And is that as far as I can take the solution with the radicals, or is there a further step?

 

[Denis]

For the 30-60-90 triangle, would the shorter side, which is n, then be 8 divided by root 3? Making the hypotenuse 2 times (8 divided by root 3)? And is that as far as I can take the solution with the radicals, or is there a further step?

Correct. No further step. Hypotenuse = 16 / sqrt(3)
Why are you not sure?