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Tamara is flying in a hot air balloon. The hot air balloons is flying at an altitude of 1100 feet. The ground distance to the landing site is 1400 feet.
What is Tamara's angle of depression to the landing site?
What is the actual distance between the hot air balloon and the landing site?

  • pre cal -

    If you sketch this out you will have a right triangle, I will call ABC.

    A is the vertex = angle of depression
    AC (side b) = base = 1400 feet
    BC (side a) = leg = 1100 feet
    AB (side c) = hypotenuse = distance to landing site

    To find angle A (angle of depression)
    tan A = a/b = 1100/1400 = 0.7857
    tan A = 0.7857
    arctan 0.7857 = 38.16 deg

    To find C (distance to airport)
    c^2 = a^2 + b^2
    c^2 = 1100^2 + 1400^2
    c^2 = 1,210,000 + 1,960,000
    c^2 = 3,170,000
    c = 1780.45 feet

    1780.45/5280 feet in mile = 0.34 miles

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