Jasmine the Great Dane has a head 30 cm long. Her tall is equal to the size of her head plus one-half the size of her body. Her body is the size of her head phluss the tal. How long is Jasmine? ​

240 cm

Step-by-step explanation:

Let x = tail   y = body

x = 30 + 1/2y

y = 30 + x

Let's plug in the x equation at the bottom

y = 30 + 30 + 1/2y

y = 60 + 1/2y

Bring the like terms to one side

y = 60 + 1/2y

-1/2y    -1/2y

1/2y = 60

Multiply both sides by 2 to get the length of the body

1/2y x 2 = 60 x 2

y = 120

Now we can plug in the new y into another equation, let's use the top one

x = 30 + 1/2(120)

x = 30 + 60

x = 90 = length of the tail

Add em all up

120 + 90 + 30 = 240

11.2

step-by-step explanation:

when doing tangent the tangent of the angle is equal to the opposite side from the angle over the adjacent side to the angle.

tan43 = x / 12

move 12 over by multiplying each side by 12

12tan43 = x

x = about 11.2

< 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)