Chapter 8: Q. 63 (page 536)
State the Law of Cosines in words.
The Law of Cosines states that the square of one side of a triangle equals the sum of the squares of the other two sides minus twice their product times the cosine of their included angle.
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an object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that the motion is simple harmonic with period T, write an equation that relates the displacement d of the object from its rest position after t seconds. Also assume that the positive direction of the motion is up:
Circumscribing a TriangleShow that
where is the radius of the circle circumscribing the triangle PQR whose sides are a, b, and c, as shown in the figure.
Given only the three sides of a triangle, there is insufficient information to solve the triangle .
Constructing a Highway U.S. 41, a highway whose primary directions are northโsouth, is being constructed along the west coast of Florida. Near Naples, a bay obstructs
the straight path of the road. Since the cost of a bridge is prohibitive, engineers decide to go around the bay. The illustration shows the path that they decide on and the measurements taken. What is the length of highway needed to go around the bay?
Rework Problem 7 under the same conditions except that, at time t = 0, the object is at its resting position and moving down.
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