SOLUTION: Find the longer leg of a 30-60-90 triangle if its hypotenuse is 2√3.

Algebra.Com
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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