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From lookout tower 80ft. high, a man observes from a position 6.5 ft. below the top of the tower that the angle of elevation of the top of the certain tree is 12deg40mins and the angle of depression of its base is 70deg20mins. If the base oof the tower and the base of the tree are the same level, what is the height of the tree?

  • trigonometry -

    I will help you with the diagram, after that it is easy.

    Draw a vertical line AB, the tower, where A is the position of the man and B is the base of the tower.
    AB = 73.5

    Draw another vertical line CD, for the tree, C as the top and D as the bottom
    Mark E on CD as the same height as AB
    clearly AE = BD
    and ED = AB , all we need is CE

    angle (CAE) = 12.66667°
    angle(EAD) = 70.3333° making angle (BAD) = 19.66667°

    You now have 2 nice right-angled triangles, where you can find BD, and its an easy ride after that

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