Najpierw obliczymy cosinus zaznaczonego kąta:
[tex]|BC|^2=|AB|^2+|AC|^2-2\cdot|AB|\cdot|AC|\cdot \cos\alpha\\\\16^2=14^2+20^2-2\cdot14\cdot20\cdot\cos\alpha\\\\256=196+400-560\cos\alpha\\\\256=596-560\cos\alpha\\\\560\cos\alpha=340\\\\\cos\alpha=\dfrac{17}{28}[/tex]
Ponownie korzystamy z twierdzenia cosinusów:
[tex]|CD|^2=|AD|^2+|AC|^2-2\cdot|AD|\cdot|AC|\cdot\cos\alpha\\\\x^2=7^2+20^2-2\cdot7\cdot20\cdot\dfrac{17}{28}\\\\x^2=49+400-170\\\\x^2=279\\\\\boxed{x=3\sqrt{31}\ [\text{cm}]}[/tex]
