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Rajan@2021
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A man on the deck of a ship, 16 m above water level, observe that that angle of elevation and depression respectively of the top and bottom of a cliff are 60° and 30° . Calculate the distance of the cliff from the ship and height of the cliff.

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An important question from trigonometry (height and distance) in which we have to find the distance of the cliff from the ship and the height of the cliff if a man on the deck of a ship, 16 m above water level, observe that that angle of elevation and depression respectively of the top and bottom of a cliff are 60° and 30°.

Class 10, RS Aggarwal, Chapter 14, qquestion no 23

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  1. This answer was edited.

    Consider A as the man on the deck of a ship B and CE is the cliff,
    Then AB=16m
    Given
    Angle of elevation from the top of the cliff = 45o
    Angle of depression at the base of the cliff = 30o

    Take CE=h and AD=x
    Then, CD=h−16  and  AD=BE=x

    In right triangle CAD
    tanθ=CD/AD​
    Substituting the values,
    ⇒tan45°=(h−16)/x​
    So, we get
    ⇒1=(h−16)/x​
    ⇒x=h−16…………..(1)

    In right △ADE
    tanθ=DE/AD​
    Substituting the values,
    ⇒tan30°=16/x​
    So, we get
    ⇒31/√3​=16/x​
    ⇒x=16√3…………..​(2)

    Using both the equations
    h−16=16√3​
    ⇒h=16√3​+16
    ⇒h=16(1.732+1)
    ⇒h=16(2.732)
    ⇒h=43.712=43.71 m

    Substituting the value in equation (1)
    x=h−16
    ⇒x=43.71−16
    ⇒x=27.71

    Hence, the distance of cliff = 27.71m.
    An the height of cliff = 43.71m.

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