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Pre-Calculus-Trig

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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.

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