Question

Where is the orthocenter of obtuse triangle CDE located? Find GD.

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

Answer 1

The orthocenter is where the altitudes meet. Based on that, can you tell me where the orthocenter is?

Answer 2

it will be (5x+55) degrees

Answer 3

Well, the 5x+55 is at a right angle. So, the equation you want to solve for x is 5x + 55 = 90 since it's a right angle.

Answer 4

it will be 2x-9

Answer 5

Ok, GD = 2x - 9, yes. However, to solve for GD, we need to solve for what 'x' is to plug in. The only information that lets us solve for what x is that 5x5 + 55 is a right angle. This means that \(5x+55=90\). Can you solve for what \(x\) is?

Answer 6

is x=7

Answer 7

There you go. Now, you can plug it into GD to solve for GD.

Answer 8

so it will be c right?

Answer 9

Not quite. You solved for what x is. However, GD = 2x - 9. So now, you need to plug in what x is. So, evaluate: \(2(7)-9\).

Answer 10

so its a

Answer 11

Yes. And you know that the orthocenter is outside of the triangle because CDE is an obtuse triangle, which means the altitudes intersect outside of the triangle. Good job.

Answer 12

Thanks