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Chapter 8: Q. 31 (page 554)
Finding the Grade of a Mountain Trail A straight trail with a uniform inclination leads from a hotel, elevation 5000 feet, to a lake in a valley, elevation 4100 feet. The length of the trail is 4100 feet. What is the inclination (grade) of the trail?
The trail is about from lake to hotel
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Distance to the Moon At exactly the same time, Tom and Alice measured the angle of elevation to the moon while standing exactly 300 km apart. The angle of elevation to
the moon for Tom was 49.8974掳 and the angle of elevation to the moon for Alice was 49.9312掳. See the figure. To the nearest 1000 km, how far was the moon from Earth when
the measurement was obtained?
Chicago SkyscrapersThe angle of inclination from the base of the John Hancock Center to the top of the main structure of the Willis Tower is approximately 10.3掳. If the main structure of the Willis Tower is 1450 feet tall, how far apart are the two skyscrapers? Assume the bases of the two buildings are at the same elevation.
If three sides of a triangle are given, the Law of _________ is used to solve the triangle.
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?
A cruise ship maintains an average speed of knots in going from San Juan, Puerto Rico, to Barbados, West Indies, a distance of nautical miles. To avoid a tropical storm, the captain heads out of San Juan in a direction of off a direct heading to Barbados. The captain maintains the - knot speed for hours, after which the path to Barbados becomes clear of storms.
(a) Through what angle should the captain turn to head directly to Barbados?
(b) Once the turn is made, how long will it take before the ship reaches Barbados if the same -knot speed is maintained?
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