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Chapter 8: Q. 2 (page 527)
If is an acute angle, solve thee equation.
The solution is.
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For any triangle, derive the formula
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?
Area of an ASA Triangle If two angles and the included side are given, the third angle is easy to find. Use the Law of Sines to show that the area K of the triangle with side and angles A, B, and C is
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.]
Given only the three sides of a triangle, there is insufficient information to solve the triangle .
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