SOLUTION: Given the hypotenuse of a 30 - 60 - 90 degrees triangle, determine the lengths of the two legs. Write your answers as radicals in simplest form. Answer this where: c = hypoten

Algebra ->  Triangles -> SOLUTION: Given the hypotenuse of a 30 - 60 - 90 degrees triangle, determine the lengths of the two legs. Write your answers as radicals in simplest form. Answer this where: c = hypoten      Log On


   

Question 668543: Given the hypotenuse of a 30 - 60 - 90 degrees triangle, determine the lengths of the two legs. Write your answers as radicals in simplest form.
Answer this where:
c = hypotenuse
hypotenuse = 6 sqrt 3
a = ?
b = ?
Found 2 solutions by swincher4391, MathLover1:
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
If we have a 30,60,90 triangle where a,b,c are the lengths from smallest to largest then we have that
a = a
b = sqrt(3)*a
c = 2a
So c = 6 * sqrt(3), a is half of that giving us 3*sqrt(3), and b is 3*sqrt(3)*sqrt(3) = 3 * 3 = 9
a = 3*sqrt(3)
b = 9
c = 6*sqrt(3)

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

h=+6sqrt%283%29
a= long leg across from 60º
b = short leg across from 30º
_______________________________________
then a=%281%2F2%29h%2Asqrt%283%29
b=%281%2F2%29h
_______________________________

a=%281%2F2%296sqrt%283%29%2Asqrt%283%29
a=%281%2F2%296%28sqrt%283%29%29%5E2
a=%281%2Fcross%282%29%29cross%286%293%2A3
a=9


b=%281%2F2%29h
b=%281%2Fcross%282%29%29cross%286%293sqrt%283%29
b=3sqrt%283%29
if you plug in value of sqrt%283%29=1.73, then you have
h=+6%2A1.73
highlight%28h=10.39%29
highlight%28a=9%29
b=3%2A1.73
highlight%28b=5.19%29
now check using Pythagorean theorem:
h%5E2=a%5E2%2Bb%5E2
%2810.39%29%5E2=9%5E2%2B%285.19%29%5E2

107.95=81%2B26.94
107.9521=107.94...round to whole numbers
108=108