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Chapter 8: Q.7 (page 553)
Solve each triangle.
The value of
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Given two sides and the included angle, the first thing to do to solve the triangle is to use the Law of Sines .
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:
Mollweide’s Formula For any triangle, Mollweide’s Formula (named after Karl Mollweide, 1774–1825) states that
Derive it.
[Hint: Use the Law of Sines and then a Sum-to-Product Formula. Notice that this formula involves all six parts of a triangle. As a result, it is sometimes used to check the solution of a triangle.]
The tallest tower built before the era of television masts, the Eiffel Tower was completed on March 31, 1889. Find the height of the Eiffel Tower (before a television mast was added to the top) using the information given in the illustration.
In the given problem solve the triangle using either the law of sines or law of cosines-
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