Question

where is the orthocenter of obtuse triangle CDE located? find GD.

A. outside the triangle. GD=5
B. inside the triangle. GD=5
C. outside the triangle. GD=7
D. inside the triangle. GD=7

Answer 1

We know that EGC is the supplementary angle of CGD, so:
∠EGC=180∘−∠CGD=180∘90∘=90∘
But we are also told that:
EGC=(5x+55)∘
So we can say:
(5x+55)∘=90∘5x+55=905x=90−55=35x=355=7
So:
GD=2x−9=2⋅7−9=14−9=5

Answer 2

Also, for obtuse triangles the orthocenter will be outside the triangle:

http://www.mathopenref.com/triangleorthocenter.html

Answer 3

thank you so much!