Chapter 8: Q. 49 (page 516)
Find the distance from A to C across the gorge illustrated in the figure.

Short Answer
The distance from A to C is.
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Chapter 8: Q. 49 (page 516)
Find the distance from A to C across the gorge illustrated in the figure.

The distance from A to C is.
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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° and 35°. 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?
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.]
Approximating the Area of a Lake To approximate the area of a lake, Cindy walks around the perimeter of the lake, taking the measurements shown in the illustration. Using this technique, what is the approximate area of the lake?
[Hint: Use the Law of Cosines on the three triangles shown and then find the sum of their areas.]
When a mass hanging from a spring is pulled down and then released, the motion is called __________ . if there is no frictional force to retard the motion, and the motion is called ______ if there is friction.
Constructing a Highway A highway whose primary directions are north-south 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?

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