Math - Trigonomety

A plane is flying at a height of 1000 feet. A passenger on the plane sees a tree and realizes the angle of depression to the top of the tree is 15 degrees and the angle of depression to the bottom of the tree is 25 degrees. How tall is the tree?

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  1. What a silly and unrealistic problem,
    anyway ....

    I made a sketch
    the main working triangle has the height of the tree, its opposite angle as 10°, and the other angles as 105° and 65°
    The side opposite the 105° is also the hypotenuse of a right-angled triangle with vertical side 1000 and base angle 25° (alternate angle to your angle of depression)
    let that hypotenuse be h
    sin25 = 1000/h
    h = 1000/sin25 = 2366.2

    now in the other triangle, by the sine law
    tree/sin10 = 2366.2/sin105
    tree = 2366.2sin10/sin105 = 425.4 ft

    wow !

    Since the tallest trees in the world, the sequoias of the west coast all are less than 400 ft ..........

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