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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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Finding the Distance to Shore The Willis Tower in Chicago is 1454 feet tall and is situated about 1 mile inland from the shore of Lake Michigan, as indicated in the figure on the top right. An observer in a pleasure boat on the lake directly in front of the Willis Tower looks at the top of the tower and measures the angle of elevation as 5掳. How far offshore is the boat?
Consult the figure, which shows a circle of
radius r with center at O. Find the area K of the shaded region as a function of the central angle
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?
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?
Finding the Length of a Ski Lift Consult the figure. To find the length of the span of a proposed ski lift from P to Q, a surveyor measures DPQ to be 25掳 and then walks off a
distance of 1000 feet to R and measures PRQ to be 15掳. What is the distance from P to Q?
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