Question

Please can someone help.

Answer 1

CD = 12.7 cm

Explanation:

`\text{Use the Pythagorean theorem to calculate the length of the CB:}\\\\CB^2+BA^2=AC^2\\\\CB^2+6^2=12^2\\\\CB^2+36=144\qquad\text{subtract 36 from both sides}\\\\CB^2=108\to CB=√(108)\\\\CB=√(36\cdot3)\qquad\text{use}\ √(ab)=√(a)\cdot√(b)\\\\CB=√(36)\cdot\sqrt3\\\\CB=6\sqrt3`

`\text{Use sine to calculate the length of CD:}\\\\sin\theta=(opposite)/(hypotenuse)\\\\\theta=55^o\\opposite=6\sqrt3\\hypotenuse=CD\\\\\sin55^o\approx0.8192\qquad(look\ at\ the\ picture)\\\\\text{Substitute:}\\\\0.8192=(6\sqrt3)/(CD)\\\\0.8192=(10.3923)/(CD)\qquad\text{multiply both sides by}\ CD\\\\0.8192CD=10.3923\qquad\text{divide both sides by 0.8192}\\\\CD\approx12.7`