Question

Find the missing side length leave your answers as radicals in the simplest form.

Answer 1

Part 1)
`x=(10√(3))/(3)\ units`

Part 2)
`y=5\ units`

Explanation:

step 1

Find the value of x

In the right triangle of the figure

`sin(30^o)=((5√(3)/3))/(x)` ---> opposite side angle of 30 degrees divided by the hypotenuse

Remember that

`sin(30^o)=(1)/(2)`

substitute

`(1)/(2)=((5√(3)/3))/(x)`

solve for x

`x=(5√(3))/(3)(2)`

`x=(10√(3))/(3)\ units`

step 2

Find the value of y

In the right triangle of the figure

`cos(30^o)=(y)/(x)` ---> adjacent side angle of 30 degrees divided by the hypotenuse

we have

`x=(10√(3))/(3)\ units`

`cos(30^o)=(√(3))/(2)`

substitute

`(√(3))/(2)=(y)/((10√(3))/(3))`

`y=((√(3))/(2))((10√(3))/(3))`

`y=5\ units`