geometry

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The Hubble Space Telescope is orbiting Earth 600 km above Earth's surface. Earth's radius is about 6370 km. Use the Pythagorean Theorem to find he distance a from the telescope to Earth's horizon. Round your answer to the nearest ten kilometers.

  • geometry -

    Draw the figure. Note it is a right triangle, with hypotenuse of (Rearth+altitude), legs of Rearth, and of what you want to find.

  • geometry -

    There is a right trangle formed by points at the center of the Earth, the HST satellite and the point where a line from the satellite is tangent to the Earth. The hypotenuse (c) goes from the HST to the center of the Earth, and its length is 600 + 6370= 6970 km. The side that you want is
    b^2 = c^2 - a^2, where a is the radius of the Earth.

  • geometry -

    b^2 = (6970)^2 - (6370)^2
    = 8.004*10^6
    b = 2829 km

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