Question

4.solve for x and y
pls help

Answer 1

x = 4
`√(3)`

y = 8
`√(3)`

Explanation:

this is a 30-60-90 triangle and the sides have a constant ratio

the side across from the 30°∡ is 1

the side across from the 60°∡ is √3

the side across from the 90°∡ is 2

In this problem we can find 'x' by setting up this proportion:

x/12 =
`√(3)`/1

cross-multiply:

`√(3)`x = 12

x = 12/
`√(3)`

since we don't like to leave radicals in the denominator, we can multiply both numerator and denominator by
`√(3)` to get:

12
`√(3)` ÷
`√(3)`·
`√(3)` (
`√(3)`·
`√(3)` =
`√(9)`, which equals 3)

so we have 12
`√(3)`/3, which is 4
`√(3)`

The 'y' value will be twice the 30° side, so 8
`√(3)`