Post a New Question

Pre-Calculus-Trig

posted by .

A surveyor stakes out points A and B on sides of a building. Point C on the side of the building is 300 feet from A and 440 feet from B. Angle ACB measures 38 degrees. What is the distance from A to B?

  • Pre-Calculus-Trig -

    Use the Law of Cosines to solve triangle ABC:

    cosC = (a^2 + b^2 - c^2) / 2ab.

    cos38=((440)^2+(300)^2-c^2)/2*440*300,
    0.7880 = (283600 - c^2) / 264000,
    Cross multiply:
    -c^2 + 283600 = 208032,
    -c^2 = 208032 - 283600,
    -c^2 = - 75568,
    c^2 = 75568,
    c = 275ft. = Distance from A to B.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    Two points A and B are on opposite sides of a building. A surveyor selects a third point C to place a transit Point C is 47 feet from point A and 64 feet from point B. The angle ACB is 56 degrees. How far apart are points A and B?
  2. Pre Calc

    To determine the height of the Louisiana-Pacific (LP) Tower, the tallest building in Conroe, Texas, a surveyor stands at a point on the ground, level with the base of the LP building. She measures the point to be 320ft from the building's …
  3. Pre-Calculus

    1.The angle of elevation to top of a building from a point on the ground 20degrees and the angle of elevation from a point to 25 feet farther away is 12degrees. Find the height of the building. 2.From a point on the ground, the angle …
  4. college Trig

    To find the distance from the house at A to the house at B, a surveyor measures the angle ACB, which is found to be 70°, and then walks off the distance to each house, 50 feet and 70 feet, respectively. How far apart are the houses?
  5. Trigonometry

    A hill in Colorado makes an angle of 15.0° with the horizontal and has a building at the top. At a point 75.0 feet down the hill from the base of the building, the angle of elevation to the top of the building is 55.0°. What is the …
  6. Trig

    From a point 120 feet from the base of a plant building the angle of elevation to the roof line of the building is 38 degrees. The angle of elevation to the top of an antenna is 43 degrees. The antenna is attached to the nearest edge …
  7. Per Calculus

    A surveyor is standing 50 feet from the base of a building. The angle of elevation to the top of the building is 60 degrees. Approximately how tall is the building?
  8. Pre-Calculus

    A surveyor measures the distance between buildings X and Y as 200 feet. The angle of elevation from the base of X to the top of Y is 25 degrees. What is the height of building Y?
  9. math

    Sighting the top of a building, a surveyor measured the angle of elevation to be 60°. The measurement is taken 200 feet from the building. Find the building’s height. Express your answer in terms of feet and then round to two decimal …
  10. Pre-calculus

    A surveyor standing 62 meters from the base of a building measures the angle to the top of the building and finds it to be 38°. The surveyor then measures the angle to the top of the radio tower on the building and finds that it is …

More Similar Questions

Post a New Question