Question

where is the orthocenter of obtuse triangle cde located? find gd
a. outside of triangle, gd = 5
b. inside the triangle, gd = 5
c. outside the triangle, gd = 7
d. inside the triangle, gd = 7

Answer 1

WILL GIVE MEDAL PLZZZ HELP QUICK!!

Answer 2

We know that EGC is the supplementary angle of CGD, so:
$$ \angle EGC = 180^\circ - \angle CGD = 180^\circ 90^\circ = 90^\circ
$$But we are also told that:
$$
EGC = (5x + 55)^\circ
$$So we can say:
$$
(5x + 55)^\circ = 90^\circ \\
5x + 55= 90\\
5x = 90 - 55 = 35\\
x = \frac{35}{5} = 7
$$So:
$$
GD = 2x - 9 = 2 \cdot 7 - 9 = 14 - 9 = 5
$$

Answer 3

Also, for obtuse triangles the orthocenter will be outside the triangle:
http://www.mathopenref.com/triangleorthocenter.html

Answer 4

ty!!