Question 1185237: Find the longer leg of a 30-60-90 triangle if its
hypotenuse is 2√3.
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the hypotenuse is 2 * sqrt(3).
the angles are 30, 60, and 90.
the trigonometric functions are:
sin(30) = 1/2
sin(60) = sqrt(2)/3
hypotenuse is equal to sqrt((1/2)^2 + (sqrt(3)/2)^2) = 1
if the hypotenuse is equal to 2*sqrt(3), then all sides need to be multiplied by 2*sqrt(3).
you get:
hypotenuse = 1 * 2 * sqrt(30 = 2 * sqrt(30
side opposite 30 degree angle = 1/2 * 2 * sqrt(30 = sqrt(3)
side opposite 60 degree angle = sqrt(3)/2 * 2 * sqrt)30 = 3
the sum of the sides squared must be equal to the the square of the hypotenuse.
(2 * sqrt(3))^2 = sqrt(3)^2 + 3^2.
simplify to get:
12 = 3 + 9 which becomes:
12 = 12
this confirms the new sizes of the legs are correct when the hypotenuse is equal to 2 * sqrt(3).
the longest leg would be the leg whose length is equal to 3.
here's a reference on 30, 60, 90 degree triangle.
https://blog.prepscholar.com/30-60-90-triangle-ratio-formula
they get the same result a different way.
one of their examples is the triangle whose hypotenuse is 2 * sqrt(3).
you coculd have gotten the answer either way.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
Find the longer leg of a 30-60-90 triangle if its
hypotenuse is 2√3.
For a 30-60-90 triangle, the LONGER LEG'S measure, using the hypotenuse's measure, is found by merely MULTIPLYING the HYPOTENUSE by  .
Therefore, in this case, 
That's ALL!! This is NOT that COMPLICATED, at all!
**Note: If you don't know the above, then you need to read up on it.
And, while you're at it, look up how to find the measures of the sides of 45-45-90 triangles.
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