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Chapter 8: Q. 3 (page 534)
If three sides of a triangle are given, the Law of _________ is used to solve the triangle.
The solution is Cosines.
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an object of mass m (in grams) attached to a coiled spring with damping factor b (in grams per second) is pulled down a distance a (in centimeters) from its rest position and then released. Assume that the positive direction of the motion is up and the period is T (in seconds) under simple harmonic motion.
(a) Develop a model that relates the distance d of the object from its rest position after t seconds.
(b) Graph the equation found in part (a) for 5 oscillations using a graphing utility.
Given values:
Calculating Distances at Sea The navigator of a ship at sea spots two lighthouses that she knows to be 3 miles apart along a straight seashore. She determines that the angles formed between two line-of-sight observations of the lighthouses and the line from the ship directly to shore are 15掳 and 35掳. See the illustration.
(a) How far is the ship from lighthouse P?
(b) How far is the ship from lighthouse Q?
(c) How far is the ship from shore?
Venus The distance from the Sun to Earth is approximately 149,600,000 km. The distance from the Sun to Venus is approximately 108,200,000 km. The elongation angle is the angle formed between the line of sight from Earth to the Sun and the line of sight from Earth to Venus. Suppose that the elongation angle for Venus is 10掳. Use this information
to find the possible distances between Earth and Venus.
A 22-foot extension ladder leaning against a building makes a 70掳 angle with the ground. How far up the building does the ladder touch?
Time Lost due to a Navigation Error In attempting to fly from city P to city Q, an aircraft followed a course that was 10掳 in error, as indicated in the figure. After flying a distance
of 50 miles, the pilot corrected the course by turning at point R and flying 70 miles farther. If the constant speed of the aircraft was 250 miles per hour, how much time was lost due
to the error?
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