Question

Pls help I don’t understand this question very well

Answer 1

`CD = 12.6866616739cm`

`CD \approx12.7cm`

Explanation:

`CB = a`

`AB = b`

`AC = c`

`{c}^(2) = {a}^(2) + {b}^(2)`

`{a}^(2) = {c}^(2) - {b}^(2)`

`a = \sqrt{ {c}^(2) - {b}^(2) }`

`a = \sqrt{ {12}^(2) - {6}^(2) }`

`a = √(144 - 36)`

`a = √(108)`

`CB = √(108)`

`\sin(D) = (opposite)/(hypotenuse)`

`\sin(D) = (CB)/(CD)`

`\sin(55) = ( √(108) )/(CD)`

`(CD) \sin(55) = ( √(108) )/(CD) (CD)`

`(CD) \sin(55) = √(108)`

`((CD) \sin(55) )/( \sin(55) ) = ( √(108) )/( \sin(55) )`

`CD = ( √(108) )/( \sin(55) )`

`CD = 12.6866616739cm`

`CD \approx12.7cm`