Math

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which mountains peaks can be seen from Oahu.

Island Distance(Mi) Mountain Height(ft)
Molokai - 40 - Kamakou - 4,961

A) Radius of earth= 3960 mi.
Determine angle formed at the center of the earth.
B) Determine length of the hypotenuse.

Could someone go through the steps to solve this?

I have already done so but I seem to get close but different answers I need to check my work.

  • Math -

    Assume that the observer is at sea-level.

    The horizontal line is tangent to the earth at Oahu,
    distance = 40 miles = 40*5280'=211200'

    The radius of the earth is
    r=3960 miles=20908800'
    and is perpendicular to the horizontal line above.

    Hypotenuse
    =sqrt(211200²+20908800²)
    =2745600√(58)'
    Visible height
    = hypotenuse - radius of earth
    = 1066.64' < 4961
    Therefore the said peak is visible.

  • Math -

    So the question is basically asking which mountains peaks can be seen from Oahu.

    Island Distance(Mi) Mountain Height(ft)
    Lanai - 65 - Lanaihale - 3,370
    Maui - 110 - Haleakala - 10,023
    Hawaii - 190 - Mauna Kea - 13,796
    Molokai - 40 - Kamakou - 4,961

    A) Radius of earth= 3960 mi.
    Determine angle formed at the center of the earth.
    B) Determine length of the hypotenuse.
    Is Lanai-hale visible from Oahu?
    C) Repeat parts A & B for the other 3 islands
    D) Which 3 Mountains are visible from Oahu?
    Can someone draw me a diagram and explain to me what to do step by step? please and thank you!!

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