Math

1. A rangers tower is located 44m from a tall tree. From the top of the tower, the angle of elevation to the top of the tree is 28 degrees and the angle of depression to the base is 36 degrees. How tall is the tree?

2. An engineer determines that the angle of elevation from her position to the top of the tower is 52 degrees. She measures the angle of elevation again from the point 47m far from the tower and finds it to be 31 degrees. Both positions are due east of the town. Find the height of the tower.

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  1. 1.
    height of tree above her line of sight:
    h1/44 = tan28
    h1 = 44tan28

    height of tree below her line of sight:
    h2/44 = tan36
    h2 = 44tan36

    height of tree = h1 + h2 = ...

    (not a good idea to have her view to be below the tree line)

    2. make a sketch. Label the top of the tree T, her first position B and her second position A
    angle A = 31
    angle TBA = 128
    then angle BTA = 21°

    At this point I suspect a typo. The usual distance given for this type of question is the distance between here two observation points.
    The way you have it, we could simply do:
    height of tower/47 = tan 52
    height of tower = 47tan52 = ....
    and all the other stuff would not be needed.

    Before I proceed , please confirm which way the wording should be.

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  2. 83.95

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  3. in Lenin Square.

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  4. yea

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