math

posted by .

a pole leans away from the sun at an angle of 7 degrees to the vertical. when the elivation of the sun is 48 degrees the pole cast a shadow of 41ft long on level ground. how long is the pole?

  • math -

    a is vertically under pole, base to tip
    41 - a is shadow tip from under pole tip

    height of pole = y cos 7 = .993 y
    tan 48 = .993 y/(41-a)

    tan 7 = a/y so a = y tan 7

    then
    tan 48 = .993 y/(41 -y tan 7) solve for y

  • math -

    Draw a big diagram

    You end up with a triangle with:

    the horizontal side = 47 ft

    the side representing the leaning pole ... call it a

    and the angle opposite the pole side = 51°



    The pole makes an angle of 7° with the vertical ... so the angle between to pole side and the 47ft side = 90 - 7 = 83°

    So that make the angle opposite the 47 ft side = 180 - (51 + 83) = 46°


    Now you can use the sine rule to find the length of the pole:

    a/sin51° = 47/sin46

    a = 47 * sin51 / sin46

    a = 50.8 ft

    so the length of the pole is 50.8 ft

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Trigonometry

    the leaning tower of pisa is 179 ft tall. it leans at an angle of 5.5 degrees. if the angle of elevation of the sun is 60 degrees and the sun is opposite the side on which the tower leans, how long is the shadow that the tower will …
  2. trig

    This a problem I need help with. A vertical ple stands by a road that is inclined 10 degrees to the horizontal. When the angle of elevation of the sun is 23 degrees, the pole casts a shadow 38 ft long directly downhill along the road. …
  3. Pre-Calculus-Trig

    A pole tilts 12 degrees from the vertical, away from the sun, casts a 34 foot long shadow on level ground. The angle of elevation from the end of the shadow to the top of the pole is 64 degrees. How long is the pole?
  4. calculus

    A pole at a right angle to the horizontal is located on a slope that makes an angle of 12 degrees with the horizontal. The pole's shadow is 16 meters long and points up the slope. The angle of elevation from the tip of the shadow to …
  5. calculus

    A straight road makes an angle, A of 12 degrees. When the angle of elevation, B, of the sun is 55 degrees, a vertical pole beside the road casts a shadow 7 feet long parallel to the road. Approximate the length of the pole. Round to …
  6. Trigo

    A vertical pole is standing on a slope that is inclined at an angle 8 degrees to the horizontal and casts a shadow that is 82 ft. long down the slope. How tall is the pole if the angle of elevation of the sun is 28 degrees?
  7. mathematics

    a vertical pole stands on level ground. from a point on the ground, which is 15 meters away from the pole, the angle of elevation of its top is found to be 30 degrees.find the height of the pole?
  8. Trigonometry

    A pole leans away from the sun at an angle of 7° to the vertical. When the angle of elevation of the sun is 51°, the pole cast a shadow 47ft. long on level ground. How long is the pole?
  9. math

    on a sunny day, the sun ray meet the ground at an angle of 35 degrees. a pole casts a shadow 21.3m in length. how tall is the pole.
  10. trigonometry

    How to solve a vertical pole 8 feet tall cast a shadow 5 feet long on level ground.find the angle which the rays of the sun makes with the horizontal.

More Similar Questions