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

Answer:

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

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

$\cos 30=\frac{x}{11}$

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

$\sin 30=\frac{y}{11}$

multiplying both sides by 11 gives

$11\sin 30=y$

Now since

$\sin 30=\frac{1}{2}$

we have

$y=11\cdot\frac{1}{2}$$\boxed{y=\frac{11}{2}}$

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

$\text{perimeter = 11+x+y}$$perimeter=11+\frac{11}{2}+\frac{11\sqrt[]{3}}{2}$

which simplifies to give

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

which is our answer!