Find the missing side

4) d

5) a

Step-by-step explanation:

4)

Well we know we use sine when we need or have the hypotenuse or opposite side length.

X in this case is the opposite side length so.

Sin59=x/17

x=17sin(59)

x=14.5718

So the answer is d.

5)

We have the adjacent side length and we need opposite side length so use tan

tan(53)=x/12

x=12tan(53)

x=15.9245

Thus answer is a

< 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)