Angles of elevation and depression

posted by Emmanuel

The teet of two vertical poles of height 3m and 7m are in line with a point P on the ground. The smaller pole being between the taller pole and P and at distance of 20m from P the angle of elevation of the top T of the taller pole from the top R of the smaller pole is 30°.find the distance RT distance of the foot of the taller pole P correct to 3 significant figure angles of elevation of T from P to the nearest degree.

  1. MathMate

    In geometry problems, we need to start drawing a sketch according to instructions.
    On the sketch, label the unknowns, and hence deduce the equations/formulas that may help to solve the problem.
    Start by sketching according to given information.

    Geometry will always be difficult if one does not have the habit or skill of drawing a sketch to display given information.

    To draw the sketch, analyse sentences one at a time. I'll get you started:
    "The teet of two vertical poles of height 3m and 7m are in line with a point P on the ground. "

    Draw three points along a horizontal line. Name the left most point P.

    "The smaller pole being between the taller pole and P and at distance of 20m from P"

    From the middle point, draw a vertical line (upwards) for the 3m pole, and from the rightmost point, draw a vertical line for the 7m pole. Mark 20m between point P and the smaller (3m) pole.

    " the angle of elevation of the top T of the taller pole from the top R of the smaller pole is 30°"

    Name the top of the 7m pole T, and the top of the 3m pole R.
    The angle of elevation from R to T is 30°. Mark that on your diagram.

    Now for the solution part, draw a horizontal line through R to intersect the 7m pole at S.

    Extract the right triangle RST and indicate the known measurements:
    angle of elevation = 30 degrees
    height ST=7-3=4m
    angle RST=90 degrees.

    Hence we have a right triangle of which two of the dimensions are known. Solve for the distance (adjacent side to 30°) RS.

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