S.O.S. Mathematics CyberBoard

how tall would a person on earth have to be to see 7 miles to the horizion? I KNOW THE RADIUS OF EARTH IS ABOUT 3963 MILES. WHAT FORMULA DO I USE AND HOW

Draw a circle, with center O. Draw a radius OM to the point where the Man is standing on. Extend this radius from point M to a point H to represent the Men's Height. Now draw a tangent to the circle through H. Find the intersection I between this tangent and the circle.

The angle OÃŽH is right. In triangle OIH we have OI = 3963, IH = 7, and OH = (3963 + h), h being the Men's Height.

Now you can use the Pythagorean theorem (painful, with these big numbers). Or you can find one of the angles, say, HÔI, using tan (HÔI) = IH/OI (and an electronic calculator, I guess). And then you use cos (HÔI) = OI/IH to find OH.

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