Question

AB = 6 cm, AC = 12 cm

Answer 1

Answer:

12.7cm

Step-by-step explanation:

there are 2 triangles , triangle ABC and triangle BCD

use Pythagoras theorem for triangle ABC to find the line BC

let BC = h

12^2=6^2+h^2

making h the subject

h=

$\sqrt{ {12}^{2} - {6}^{2} }$

h =

$6 \sqrt{3}$

so line BC is

$6 \sqrt{3}$

for triangle BCD, there's an angle 55 degrees

sin theta = opposite/hypotenuse

where BC is the opposite

theta which is the angle = 55

$h = \frac{6 \sqrt{3} }{sin55}$

$sin55 = \frac{6 \sqrt{3} }{h}$

$h = 12.69$

note h = CD

in 3 s.f ,h= 12.7cm