Triangle ABC has AB=BC, AC = 16, and angle B = 90 degrees. AC is extended to D such that BD=17. Find the length of CD.
+128407 Triangle ABC is a 45-45-90 right triangle
BC =16/sqrt (2) = 8sqrt (2) = sqrt ( 128)
Angle BCD = 180 - 45 = 135°
Using the Law of Cosines
BD^2 = CD^2 + BC^2 - 2( CD * BC) cos (135°)
289 = CD^2 + 128 - 2 (CD * 8sqrt (2)) ( - sqrt (2) / 2)
289 - 128 = CD ^2 + 16CD
161 = CD^2 + 16CD
CD^2 + 16CD - 161 = 0 factor
(CD + 23) ( CD -7) = 0
The second factor set = 0 and solved gives us that CD = 7
