this is a topic of plane geometry and we were given a directed investigation 'How far can you see the horizon?' this is it....the circle represents a cross-section of the Earth. imagine you are in a balloon at B. BT shows the furthest point, T, on the Earth's surface that you could see. imagine that you have just dropped a very heavy, sharp object from your balloon. the object, hits the ground at E, directly below you, boring its way through Earth coming to a stop just as it reaches the antipodal point A.
here's a diagram: i have an attachment and its called doc. please someone answer this, its due monday and its worth 25% of my grade.
November 13th 2008, 04:36 PM
How far can you see to the horizon?
The circle represents a cross-section of the Earth.
Imagine you are in a balloon at shows the furthest point, , on the Earth's surface that you could see.
* * * \
* | *\ T
* | o
* R| * *
* | * *
* o *
* O *
* * *
The balloon is at miles above the Earth.
The center of the Earth is ; the radius is:
The angle at is 90°.
Using Pythagorus on
Therefore: . , the distance from the balloon to the horizon
. . is given by: . miles
where: . = height of balloon, = radius of the Earth (both in miles).