Find the value of the variables. if the answer is not an integer, leave it in simplest radical form.

Explanation:

The short leg is given to be 9 units long. This side is opposite the smallest angle. The rule is that smallest side is opposite the smallest angle. The hypotenuse is twice as long as the short leg in a 30-60-90 triangle, so 2*9 = 18 is the hypotenuse.

The long leg is equal to sqrt(3) times the short leg

long leg = (short leg)*sqrt(3)

long leg = 9*sqrt(3)

You can use the pythagorean theorem with a = 9 and c = 18 to solve for b

a^2 + b^2 = c^2

9^2 + b^2 = 18^2

81 + b^2 = 324

b^2 = 324 - 81

b^2 = 243

b = sqrt(243)

b = sqrt(81*3)

b = sqrt(81)*sqrt(3)

b = 9*sqrt(3)

It's a longer way to get the same answer as above for the length of the long leg.

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

your answer is the frist one

hop i