Question

the length of the hypotenuse of 30 degrees 60 degrees 90 degrees triangle is 11. what is the perimeter?(options) :a. 11/2 + 33/2 square root 3b. 33/2+ 11/2 square root 3c. 11+33 square root 3d. 33+11 square root 3

Answer 1

`\frac{33+11\sqrt[]{3}}{2}`

Step-by-step explanation:

The 30/60/90 triangle is given below

The perimeter of the triangle is

`11+x+y`

therefore, we need to find the value of x and y.

The value of x is given by

`\cos 30=(x)/(11)`

multiplying both sides by 11 gives

`11\cos 30=x`

now

`\cos 30=\frac{\sqrt[]{3}}{2}`

therefore.

`\boxed{x=11\cdot\frac{\sqrt[]{3}}{2}}`

Now we fidn the value of y.

The value of y is given by

`\sin 30=(y)/(11)`

multiplying both sides by 11 gives

`11\sin 30=y`

Now since

`\sin 30=(1)/(2)`

we have

`y=11\cdot(1)/(2)`
`\boxed{y=(11)/(2)}`

with the value of x and y in hand, wecan now find the perimeter.

`\text{perimeter = 11+x+y}`
`perimeter=11+(11)/(2)+\frac{11\sqrt[]{3}}{2}`

which simplifies to give

`perimeter=\frac{33+11\sqrt[]{3}}{2}`

which is our answer!