The Rocky Mountains
"Oh my goodness! That mountain is so huge and tall!" Katie said in amazement as her family was driving closer to the Rocky Mountains in Colorado by car, to camp near the mountain and take in nature at its best. "I wonder how tall that mountain is!"
John, her brother said in a matter-of-fact tone, "Well, we could use some trigonometry to find out. All we need to do is find the angle, from the ground to the top of the mountain, at 2 different points away from the mountain."
Katie, who was only 8 at that time, went with a confused look. After a few moments, Katie asked John a question, in curiosity.
"Is it possible that the any of the angles is 0º?"
John said reassuringly, "That is not possible, the mountain is obviously taller than ground level, so what makes you think that the tall mountain actually has no height?!"
Well, let's ask you to help answer Katie's question. Can an angle, from the ground to the top of the mountain, at a point away from the mountain, ever be 0º?
Note: The Rocky Mountains at Colorado has a height of about 4401m / 14440 feet.
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1 solution
If you think about it, the Earth is round, so the ground level on Earth is not really level.
Note: The diagram below is not drawn to scale.
Let A be the center of the Earth, and C the top of the Rocky Mountains.
Around the circumference of the Earth, there is a point, D where the angle from the ground level to the top of the mountain is 0º!!
So the answer is Yes.