Question

Find the missing sides.

Answer 1

Part 3)

`x=6\ units`

`y=3\ units`

Part 4)
`x=18√(2)\ units`

Explanation:

Part 3)

step 1

Find the value of x

In the right triangle of the figure we know that

The cosine of angle of 30 degrees is equal to the adjacent side to angle of 30 degrees divide by the hypotenuse

so

`cos(30\°)=(3√(3))/(x)`

and remember that

`cos(30\°)=(√(3))/(2)`

substitute

`(√(3))/(2)=(3√(3))/(x)`

Simplify

`x=(2*3)=6\ units`

step 2

Find the value of y

In the right triangle of the figure we know that

The sine of angle of 30 degrees is equal to the opposite side to angle of 30 degrees divide by the hypotenuse

so

`sin(30\°)=(y)/(x)`

and remember that

`sin(30\°)=(1)/(2)`

substitute

`(1)/(2)=(y)/(6)`

`y=6/2=3\ units`

Part 4) Find the value of x

Applying the Pythagoras Theorem

`x^(2) =18^(2) +18^(2) \\ \\x^(2) = 324+324\\ \\x^(2)=648\\ \\x=√(648)\ units`

Simplify

`x=18√(2)\ units`