Right triangle find x

Geometry Level 3

1 solution

Chris Lewis
Apr 17, 2020

Since $ACD$ is a right-angled triangle, we have $DC=6\sqrt{17}$ by Pythagoras. Also, $\cos \angle C=\frac{4}{\sqrt{17}}$ .

Since $2\cdot BD = DC$ , $BC=9\sqrt{17}$ .

Now using the cosine rule in triangle $ABC$ we have $x^2=AC^2+BC^2-2\cdot AC \cdot BC \cdot \cos \angle C=225$

so that $x=\boxed{15}$ .

if bd=dc, and dc=6sqrt17 why is the sum only 9sqrt17 and not 12sqrt17, and the answer should be sqrt720

Boris Ivanov - 1 year, 1 month ago

The question says $DC=2\cdot BD$ .

Chris Lewis - 1 year, 1 month ago