## anonymous one year ago Challenge! Ready? the length of the hypotenuse of a 30 degrees-60 degrees-90 degrees triangle is 18. What is the perimeter?

1. anonymous

How irritating. It isn't even that hard.

2. arindameducationusc

3. anonymous

hey m8 can you help me after youre done with her? :)

4. arindameducationusc

yes... @frankwillfindyou

5. anonymous

6. Owlcoffee

Well, the excercise in not well-written because you have to specify the relative position of the angles. Any how, I'll just call them "alpha" and "beta" so you can give them any order you like and still get the answer. So you have a triangle that you don't know the catets but know the hypotenuse, you can use trigonometry to find the length of those sides: $\alpha \in \mathbb{R} / \alpha = k$ $\beta \in \mathbb{R} / \beta = C$ So, what I mean with this is that you can choose wheter k is 30 or 60 and same goes for C. So, setting that aside, and having the condition that alpha has catet "a" as opposite catet: $\sin \alpha = \frac{ a }{ 18 } \rightarrow a=18\sin \alpha$ Analogical for catet "b", supposing it's the opposite catet of beta: $\sin \beta = \frac{ b }{ 18 } \rightarrow b=18 \sin \beta$ The perimeter will be the sum of the length of all the sides of the triangle: $P _{\triangle}= (18)+(18\sin \alpha)+ (18\sin \beta)$ $P _{\triangle}=18(1+\sin \alpha + \sin \beta)$

7. anonymous

You are doing it right so far.

8. Owlcoffee

That's the answer for the possible scenarios of the triangle.

9. anonymous

|dw:1438075864983:dw|

10. anonymous

Its going to have this at the end

11. Owlcoffee

Yes, I'm pretty sure it does, but you can't ask a geometry excercise without a diagram, or at least defining the components of the triangle with letters.

12. anonymous

I know that but what is the answer?