Math: Trig

to determine the height of a pole across a road, Justin takes two measurments. he stands at Point A directly across from the bass of the pole and determines that the angle of elevation to the top of the pole is 15.3 degrees. he then walks 30m parallel to the freeway to point C, where he sees that the base of the pole and Point A are 57.5 degrees apart. From point A, the base of the pole and point C are 90 degrees apart. find the height of the pole to the nearest metre.

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  1. Let P be the top of the pole, and let Q be the base of the pole.

    Let the width of the road be w meters

    w/30 = tan 57.5°
    h/w = tan 15.3°

    so, equating the two values for w,

    30*tan57.5° = h/tan15.3°
    30*1.5696 = h/0.2736
    h = 12.88m

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