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Advanced Algebra with Trigonometry Ch 5: “Trigonometric Functions” NAME ____________________ DATE __________ PER _____ “Applications Involving Right Triangles” angle of elevation line of sight Angle of Elevation: an angle measured above the line of sight Angle of Depression: an angle measured below the line of sight angle of depression EX1] From a point 115 feet from the base of a redwood tree, the angle of elevation to the top of the tree is 64.3 . Find the height of the tree to the nearest foot. EX2] From a 60 foot observation tower on the coast, a Coast Guard officer sights a boat in difficulty. The angle of depression of the boat is 3 . How far is the boat from the shoreline? EX3] An observer notes that the angle of elevation from point A to the top of a space shuttle is 27.2 . From a point 17.5 meters further from the space shuttle, the angle of elevation is 23.9 . Find the height of the space shuttle. Advanced Algebra with Trigonometry Ch 5: “Trigonometric Functions” NAME ____________________ DATE __________ PER _____ “Applications Involving Right Triangles” 1) Television screens are measured by the length of the diagonal of the screen. Find the width of a 19-inch television screen if the diagonal makes an angle of 38 with the base of the screen. 2) The angle of elevation from a point 116 meters from the base of the Eiffel Tower to the top of the tower is 68.9 . Find the approximate height of the tower. 3) Venus rotates in a nearly circular orbit around the sun. The largest angle formed by Venus, Earth, and the sun is 46.5 . The distance from Earth to the sun is approximately 149,000,000 kilometers. What is the orbital radius r of Venus? Round the answer to the nearest million kilometers. 4) From a point 300 feet from the base of a Roman aqueduct in southern France, the angle of elevation to the top of the aqueduct is 78 . Find the height of the aqueduct. #5 Let be an acute angle of a right triangle for which cot a) Find sin . 24 . 7 b) Find sec . #6-10 Find the EXACT value of each expression. __________ 6) sin 45 cos 60 __________ 7) csc 60 sin 30 cot 45 __________ 8) csc 6 cos 3 __________ 9) cos 5 5 sin 6 3 __________ 10) sin 11 7 tan 6 4 #11-12 Convert radians to degrees or degrees to radians. __________ 11) 200 __________ 12) 7 12