Question

It would be awesome if someone could help me out with these! I'll attach an image below!!:

1. Triangle ABC is called a special right triangle. What kind of special right triangle is it?

2. Using what you know about these special triangles, calculate the length of side BC. Show your work in words or equations.

3. Use your knowledge about the relationship between side lengths of this triangle to find the length of side AC. Show your work in words or equations.

4. Find the length of the hypotenuse of the right triangle ABC (Side AB).Show work in words or equations

Answer 1

For number 1, what are the angles?

Answer 2

30-60-90, so I'm pretty sure that might be the type of triangle? @elito25

Answer 3

Yes, this triangle is a 30-60-90 right triangle. Do you know the ratio of it's sides? All 30-60-90 triangles have the same ratio of it's sides.

Answer 4

http://www.regentsprep.org/Regents/math/algtrig/ATT2/Ltri30.htm

Answer 5

I think the rule is that the length of the hypotenuse is 2 times the length of the short leg and the length of the long leg is square root of 3 times the length of the short leg!

Answer 6

Yes, now are there more triangles within? Are they special right triangles too?

Answer 7

there are two triangles, it looks to me like they're both 30-60-90, but one of them might be a similar triangle? So the lengths on that one might be proportional to the other?

Answer 8

Well, you have one side for both triangles. Can you use your ratios to find AC and BC to answer questions 2 and 3?

Answer 9

I calculated it out, and I think that BC & AC might both be 20, since both are the hypotenuse and the hypotenuse is two times the length of the short leg?

Answer 10

First, cover up one triangle and look at the other along.

Answer 11

or

Answer 12

I recommend starting with the second one.

Answer 13

Okay, I reworked the problem (for the second triangle at least) and got BC=11.55? I know I still have to find AC for the other one, but am I on the right track? @elito25

Answer 14

No, wait, would BC= 5.78 and AC= 11.55? And then I'm supposed to find the length of the hypotenuse of triangle ABC (Side AB), and I think I'd add up 11.55 & 5.78 to get 17.33? Would that seem correct?

Answer 15

Sorry, @elito25, are you still there?

Answer 16

you're correct btw, it is a 30-60-90 triangle, thus we'd apply the 30-60-90 rule

so... did you find BC yet?

Answer 17

I keep second guessing it and re-doing the problem, but right now I think that BC is 20, AC is 11.55, and the hypotenuse of triangle ABC (side AB) is also 20, do you think that's correct? @jdoe0001

Answer 18

well... how did you get... BC ?

Answer 19

because I think you're supposed to use the 30-60-90 rule

Answer 20

I figured that side AC was the short leg, BC was the hypotenuse, and AB was the long leg. I know that the short leg is 1/2 of the hypotenuse, and since I thought the short leg was 10, I figured that leg BC would be 20. @jdoe0001

Answer 21

yeap, you're correct