Latitude-Longitude SystemLos Angeles is located at 34.05° North latitude and 118.24° West longitude, and Rio de Janeiro, Brazil, is located at 22.90° South latitude and 43.23° West longitude (see figure). Assume that Earth is spherical and has a radius of 4000 miles.
(a) Find the spherical coordinates for the location of each city.
(b) Find the rectangular coordinates for the location of each city.
(c) Find the angle (in radians) between the
(d) Find the great-circle distance
(e) Repeat parts (a)–(d) for the cities of Boston, located at 42.36° North latitude and 71.06° West longitude, and Honolulu, located at 21.31° North latitude and 157.86° West longitude.
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Chapter 11 Solutions
Calculus
- Guy Wire A guy wire runs from the ground to a cell tower. The wire is attached to the cell tower 150 feet above the ground. The angle formed between the wire and the ground is 43 (see figure). (a) How long is the guy wire? (b) How far from the base of the tower is the guy wire anchored to the ground?arrow_forwardRadio Antenna A short-wave radio antenna is supported by two guy wires, 165 ft and 180 ft long. Each wire is attached to the top of the antenna and anchored to the ground at two anchor points on opposite sides of the antenna. The shorter wire makes an angle of 67 with the ground. How far apart are the anchor points?arrow_forwardAir Navigation Two planes leave an airport at approximately the same time. One plane flies 425 miles per hour at a bearing of 355, and the other plane flies 530 miles per hour at a bearing of 67 (see figure). Determine the distance between the planes after they fly for 2 hours.arrow_forward
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- Observation Wheel The High Roller, located on the Las Vegas Strip in Paradise. Nevada, is currently the largest observation wheel in the world with a diameter of 520 feet. The top of the wheel stands 550 feet above the ground. Find the height of a rider after the wheel has rotated through an angle of 110. Assume the rider boards at the bottom of the wheel.arrow_forwardSpeed Enforcement A police department has set up a speed enforcement zone on a straight length of highway. A patrol car is parked parallel to the zone, 200 feet from one end and 150 feet from the other end (see figure). (a) Find the length l of the zone and the measures of angles A and B (in degrees). (b) Find the minimum amount of time (in seconds) it takes for a vehicle to pass through the zone without exceeding the posted speed limit of 35 miles per hour.arrow_forwardMeasurement A city engineer plans to build a footbridge across a lake from point X to point Y, as shown in the picture below. To find the length of the footbridge, she draws a right triangle XYZ, with right angle at X. She measures the distance from X to Z, 800 feet, and from Y to Z, 1,000 feet. How long will the bridge be?arrow_forward
- Distance An observer in a lighthouse 350 feet above sea level observes two ships directly offshore. The angles of depression to the ships are 4 and 6.5 (see figure). How far apart are the ships?arrow_forward17-22 Pythagorean Theorem In the given right angle triangle, find the side labeled x.arrow_forward
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