## anonymous 5 years ago In a 30-60-90 triangle, the hypotenuse is 20 feet long. Find the length of the length of the long leg and the short leg

1. anonymous

short - 10 long - $10\sqrt{3}$

2. anonymous

short leg is half of the hypotenuse

3. anonymous

:))

4. sriram

20cos60=10 and 20sin60=10 *(30)^1/2

5. anonymous

@siriam: LOLwut?

6. anonymous

You can just use some formulas because the given is a special triangle.

7. anonymous

you need to trig for this. short side is half of long side because it is half of an equilateral triangle then the other side comes from pythagoras.

8. anonymous

i meant you need NO trig

9. sriram

dude 20/short side=cos60 & 20 / long side=sin60 whats wrong in it??

10. anonymous

there's nothing wrong with it, it's just the harder option.

11. anonymous

Nothing. You can just use simple equations for special triangles.

12. anonymous

nothing wrong except that the only reason you know the cosine of 60 degrees is because you know the ratios, not the other way around!

13. anonymous

short=20*sin30=10 long=20*sin60=10$\sqrt{3}$

14. anonymous

Why are you applying trigonometry on such easy questions?

15. anonymous

You can just use simple equations on special triangles.

16. anonymous

in a 30-60-90, a = short side, b = long side, c = hypotenuse c = 2a ; b = $a \sqrt{3}$

17. anonymous

i think u did it too.i have no problem with trigonometry

18. anonymous

$\text{long} \text{side}=20\text{Cos}\left[\text{ArcSin}\left[\frac{10}{20}\right]\right]=10 \sqrt{3}$$20^2=10^2+\left(10 \sqrt{3}\right)^2, 400=100+300, 400= 400$