30-60-90 triangle?

Question

what if the long leg is 12 and they want to find the short leg in 30-60-90?
what is the hypotnuse

Answer 1

short leg ==> divide by squareroot3
hypotenuse ==> multiply by 2

short leg = 12/sqrt3 = 4sqrt3
hypotenuse = 24

In general:

sides are from, small to large, in the proportion of
x : sqrt3*x : 2x

Answer 2

A 30-60-90 is half of an equilateral triangle, so the short leg would be half of the hypotenuse length.
Set up an equation like:
12^2 + (1/2*x)^2 = x^2
where x represents the length of the hypotenuse.

Answer 3

Let short leg = x
tan 60° = 12 / x
x = 12 / tan 60°
x = 12 / √3
x = 4.√3
h² = 48 + 144
h = 192
h = 64 x 3
h = 8√3

Answer 4

So, side opp 60 degrees is 12.
So hypotenuse would be 8 (sqrt 3), as (sqrt 3) / 2 times hypotenuse is 12.
Side opposite 30 degrees = 1/2 times hypo = 4 (sqrt 3)

Answer 5

Sin x = opposite/hypotneuse
Cos x = adjacent/hypotenuse

If long leg is 12, then the corresponding angle is 60 degrees. So use Sin x equation.

hypotenuse = opposite (12)/Sin 60 = 13.8

Pythagorean thereom =>
short leg= Sqrt[(13.8)^2 - (12)^2] = 6.9

Answer 6

The longest leg is = to the shortest leg times the sqrt of 3
x is shortest leg
12 = sqrt3 times x
x = 12 divided sqrt 3
Rationalize the denominator
and get
4sqrt3 for the shortest leg
The hypotenuse is the shortest leg times 2 or
8 sqrt 3

Answer 7

if it's a 30-60-90 triangle,
you can use the sine rule, A/sin a = B/ sinb
12/sin 90 = B/sin 30
Therefore, the short leg is B = 6.

Answer 8

long leg/short leg = tan 60 = sqrt(3)
long leg = 12
short leg = 12/sqrt(3)
=4sqrt(3)

sin(30) = short leg/hypotenuse
hypotenuse = 4sqrt(3)/(1/2)
= 8sqrt(3)

Answer 9

let hypot = x

sin(60) = 12/x
x = 12/sin(60)
x = 13.856406460551018348219570732047
short side = 6.9282032302755091741097853660235

Answer 10

1, 2, square root of 3. you fill in the blanks.