4.solve for x and y
pls help

x = 4

y = 8

Step-by-step 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 = /1

cross-multiply:

x = 12

x = 12/

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

12 ÷ ·    (· = , which equals 3)

so we have 12/3, which is 4

The 'y' value will be twice the 30° side, so 8

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< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)