Section: 12:30 pm or 2:00 pmA tunnel for hydroelectric power is to be constructed through a mountain from one reservoir toanother at a lower level. The distance from the top of the mountain to the lower end of thetunnel is 5.32 miles, and from the top of the mountain to the upper end of the tunnel is 2.63miles. The angles of depression of the two slopes of the mountain are 42.7° and 48.8°,respectively.42.7°48.8°2.63 mi5.32 miTunnel1. What is the length of the tunnel? State answer to two decimal places.2. What angle does the tunnel make with the horizontal? State answer to the nearest tenthof a degree.

Here, we are solving the first question and for the 2nd question post the question again. Given, A…

Answered: A tunnel for hydroelectric power is to…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section: Chapter Questions

Problem 69RE

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Leaning Windmill After a wind storm, a farmer notices that his 32-foot windmill may be leaning, but he is not sure. From a point on the ground 31 feet from the base of the windmill, he finds that the angle of elevation to the top of the windmill is 48. Is the windmill leaning? If so, what is the acute angle the windmill makes with the ground?
Height of a Balloon A hot-air balloon is floating above a straight road. To estimate their height above the ground, the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon. The angles of depression are found to be 20 and 22. How high is the balloon?
Airplane Ascent During takeoff, an airplane’s angle of ascent is 18 and its speed is 260 feet per second. (a) Find the plane’s altitude after 1 minute. (b) How long will it take for the plane to climb to an altitude of 10,000 feet?
Gateway Arch A plane is flying within sight of the Gateway Arch in St. Louis, Missouri, at an elevation of 35,000 ft. The pilot would like to estimate her distance from the Gateway Arch. She finds that the angle of depression to a point on the ground below the arch is 22. a What is the distance between the plane and the arch? b What is the distance between a point on the ground directly below the plane and the arch?
Distance Between Two Ships A pilot measures the angles of depression to two ships to be 40 and 52 see the figure. If the pilot is flying at an elevation of 35,000 ft, find the distance between the two ships.
Tracking a Satellite The path of a satellite orbiting the earth causes the satellite to pass directly over two tracking stations A and B, which are 50 mi apart. When the satellite is on one side of the two stations, the angles of elevation at A and B are measured to be 87.0 and 84.2 respectively. a How far is the satellite from station A? b How high is the satellite above the ground?
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?
Height of Cloud Cover To measure the height of the cloud cover at an airport, a worker shines a spotlight upward at an angle 75 from the horizontal. An observer 600 m away measures the angle of elevation to the spot of light to be 45. Find the height h of the cloud cover.
Johnstown Inclined Plane The Johnstown Inclined Plane in Pennsylvania is one of the longest and steepest hoists in the world. The railway cars travel a distance of 896.5 feet at an angle of approximately 35.4, rising to a height of 1693.5 feet above sea level. (a) Find the vertical rise of the inclined plane. (b) Find the elevation of the lower end of the inclined plane. (c) The cars move up the mountain at a rate of 300 feet per minute. Find the rate at which they rise vertically.
Height of a Flagpole Two people decide to estimate the height of a flagpole. One person positions himself due north of the pole and the other person stands due cast of the pole. If the two people are the same distance from the pole and 25 feet from each other, find the height of the pole if the angle of elevation from the ground to the top of the pole at each persons position is 56 (Figure 21). Figure 21
Flying kites A boy is flying two kites at the same time. he has 380ft of line out to one kite and 420ft to the other. He estimates the angle between the two lines to be 30. Approximate the distance between the kites.

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