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    Trigonometry - Oblique Triangles

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    1. Two diagonals of a parallelogram are 48 ft and 37 ft respectively. If they intersect at 40°, find the sides of the parallelogram.

    2. A flagpole stands vertically on a 13° 25' slope. 500 feet downhill from its base its top is sighted at an elevated angle of 27° 30'. Find its height.

    3. Town B is 9 miles northwest of town A, town C is 6.7 miles somewhere to the east of town B.If C is 7.6 miles from town A, what is its bearing from town B?

    4. Between two rifles 500 feet apart, the angles formed with a target are 71° 46' and 83° 21'. Find the range of the target from each rifle.

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    Solution Preview

    . Two diagonals of a parallelogram are 48 ft and 37 ft respectively. If they intersect at 40°, find the sides of the parallelogram.

    Let the parallelogram be ABCD. Let its diagonals AC and BD intersect at O. Since the diagonals of a parallelogram bisect each other, the half-lengths OA and OD are respectively 24 ft and 18.5 ft. Angle AOD = 40 deg.
    By Cosine Rule, AD^2 = OA^2 + OD^2 - 2 * OA * OD * cos AOD
    AD^2 = 24^2 + 18.5^2 - 2 * 24 * 18.5 * cos 40 = 238
    AD = 15.43 ft = BC
    Angle COD = 180 - 40 = 140 deg
    CD^2 = OC^2 + OD^2 - 2 * OC * OD * cos COD
    CD^2 = 24^2 + 18.5^2 - 2 * 24 * 18.5 * cos ...

    Solution Summary

    The expert examines trigonometry oblique triangles for parallelograms. A complete, neat and step-by-step solution is provided in the attached file.

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