The distance from horizon of earth to the point P, is one leg of right angle which is equal to 351.8 miles(rounded to nearest tenth).
What is Pythagoras theorem?
Pythagoras theorem says that in a right angle triangle the square of hypotenuse side is equal to the sum of square of other two legs of right angle triangle.
The measure of Earth radius is 3959 ml.
The distance to the earth’s horizon from point P is x.
Let the center of Earth is O.
As the line segment between the from point P to earth’s horizon is the tangent of the Earth circumference. Thus the measure of angle at horizon must be right angle as shown in the below figure.
The measure of the line segment OP is,
[tex]OP=3959+15.6\\OP=3974.6[/tex]
The line segment OP is hypotenuse side in the shown figure of right angle and the square of hypotenuse side is equal to the sum of square of other two sides of right angle triangle.Thus,
[tex]3974.6^6=x^2+3959^2\\x\cong351.80[/tex]
Thus the distance to the earth’s horizon from point P is 351.8 miles (rounded to nearest tenth).
Learn more about the Pythagoras theorem here;
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