In a 30- 60 -90 triangle where the length of the hypotenuse is 20, the shorter leg is x, and the longer leg is y. find x find y
2006-06-12 02:56:58 · 9 answers · asked by georgia_gal461 1 in Education & Reference ➔ Homework Help
First of all, look at the link in my sources... It contains a picture that will help you understand what I'm trying to explain!
If the hypotenuse is 20, you know the shorter leg (x), or the leg across from the angle that measures 30°, is half of that. You know this because of the 30°-60°-90° triangle that you will probably want to memorize for your math classes (see image). So 20*(1/2) = 10. x = 10.
Now that you have the lengths of 2 out of 3 of the sides, you COULD simply use the pythagorean theorem to solve for y. But if you have a calculater and your 30°-60°-90° triangle memorized, then you can do it easier and faster. According to the image, the ratio between the shorter leg and the longer leg is 1:rt.3 (rt.3 meaning square root of 3.) That means that all you have to do is take the length of the shorter leg, and multiply it by rt.3. Since you know the length of the shorter leg (x) is 10, this is very easy. 10*rt.3 = 17.32. y = 17.32
In conclusion, to answer your question, x = 10, y = 17.32.
You could also use sine and cosine formulas to solve this problem, but I personally like my way better. If you'd like me to explain the sin and cosine way of solving this problem, hit me w/ an e-mail and I'll help if you need it!
I hope I helped, and I hope my explanation wasn't too difficult to understand! Good luck!
2006-06-12 02:59:02 · answer #1 · answered by Cando 3 · 1⤊ 0⤋
on a 30-60-90 triangle the lengths of the sides are in the ratio 1:sqrt 3:2
If the hypotenuse is 20, then the sides are 10 and 10 sqrt 3, respectively
so x = 10 and y = 10 sqrt 3
2006-06-12 06:27:05 · answer #2 · answered by jimbob 6 · 0⤊ 0⤋
The only help I'll give you is to point out that this is a right-angle triangle and therefore you can invoke Pythagoras. That is to say, that the length of the legs is proportional to the angles opposing them per the Pythagorean Theorem, which states:
A^2 + B^2 = C^2 where C reflects the length of the hypotenuse.
2006-06-12 03:01:03 · answer #3 · answered by Veritatum17 6 · 0⤊ 0⤋
That's very easy but I won't do your simple homework ... however here are some clues ... use sinus and cosinus formules ;)
Hope this helps
Even if I loose some points on editing .... Veritatum17 you are right but not in this case because we know only the measure of the hypotenuse so Pitagora formule is useless because for using it we need at least 2 sides!! Just apply the cos and sin functions on the triangle and you will find the right values ;)
2006-06-12 03:01:14 · answer #4 · answered by Trimbitas Sorin 2 · 0⤊ 0⤋
in a 30-60-90 triangle the long leg is twice the short leg. so we have only one unknown...ie. the length of the short leg..the two sides being x and 2x respectively.
2006-06-12 03:09:52 · answer #5 · answered by Rillifane 7 · 0⤊ 0⤋
sine = opposite over hypotenuse
sine 60 = y/20
y = 20 x sine 60
cosine = adjacent over hypotenuse
cosine 60 = x/20
x = 20 x cosine 60
2006-06-12 03:11:18 · answer #6 · answered by williegod 6 · 0⤊ 0⤋
the hypotenuse is 2x, so x=10. y = x*square root of 3, so y= (about) 17.32
2006-06-12 03:26:08 · answer #7 · answered by ellenangel364 3 · 0⤊ 0⤋
sin 30= x/20 -->0.5 x 20 =X --> X = 10, cos 30 = y/20 --> 0.866 x 20 = y -->y=17.32
2006-06-12 03:05:49 · answer #8 · answered by notre_darlene 3 · 0⤊ 0⤋
use Phytagorean theorem
2006-06-12 03:02:55 · answer #9 · answered by real_jomel 2 · 0⤊ 0⤋