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- Distance at Sea From the top of a 200-ft lighthouse, the angle of depression to a ship in the ocean is 23.How far is the ship from the base of the lighthouse?arrow_forwardTake this test as you would take a test in class. When you are finished, check your work against the answers given in the back of the book. A water sprinkler sprays water on a lawn over a distance of 25 feet and rotates through an angle of 130. Find the area of the lawn watered by the sprinkler.arrow_forwardMountain Climbing Several mountain climbers are located in a mountain pass between two peaks. The angles of elevation to the two peaks are 0.84 radian and 1.10 radians. A range finder shows that the distances to the peaks are 3250 feet and 6700 feet, respectively (see figure). (a) Find the angle between the two lines. (b) Approximate the amount of vertical climb that is necessary to reach the summit of each peak.arrow_forward
- Angle of Elevation An engineer designs a 75-foot cellular telephone tower. Find the angle of elevation to the top of the tower at a point on level ground 50 feet from its base.arrow_forwardRefer to the following figure in answering Exercises 7 through 13. It may be helpful to sketch figures.When side y=side r. a. What is the value of the sine function? b. What is the value of the cotangent function? c. What is the value of the cosine function? d. What is the value of the cosecant function?arrow_forwardLeaning 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?arrow_forward
- Take this test as you would take a test in class. When you are finished, check your work against the answers given in the back of the book. Consider an angle that measures 54 radians. (a) Sketch the angle in standard position. (b) Determine two coterminal angles (one positive and one negative). (c) Convert the radian measure to degree measure.arrow_forwardHeight 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.arrow_forwardRefer to the figure below. a Find the angle opposite the longest side. b Find the area of the triangle.arrow_forward
- Albert lives in New Orleans. At noon on a summer day, the angle of elevation of the sun is 84. The window in Alberts room is 4.0 feet high and 6.5 feet wide. (Sec Figure 24.) a. Calculate the area of the floor surface in Alberts room that is illuminated by the sun when the angle of elevation of the sun is 84. b. One winter day the angle of elevation of the sun outside Alberts window is 37. Will the illuminated area of the floor in Alberts room be greater on the summer day, or on the winter day? Figure 24arrow_forwardFind the angle of elevation of a rifle barrel, if a bullet fired at 1,500 feet per second takes 2 seconds to reach a height of 750 feet. Give your answer to the nearest tenth of a degree.arrow_forwardDetermine two coterminal angles (one positive and one negative) for each angle. a. =94 b. =3arrow_forward
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