Find the length of an arc that subtends a central angle of 45 in a circle of radius 8 m. Round your answer to 3 decimal places.

Transcription

1 Chapter 6 Practice Test Find the radian measure of the angle with the given degree measure. (Round your answer to three decimal places.) 80 Find the degree measure of the angle with the given radian measure: The measure of an angle in standard position is given. Find two positive angles and two negative angles between -720 and 1080 that are coterminal with the given angle. The measures of two angles in standard position are given. Determine whether the angles are coterminal. -10, 350 Find an angle between 0 and 2π that is coterminal with the given angle. Give your answer in terms of π: Find the length of an arc that subtends a central angle of 45 in a circle of radius 8 m. Round your answer to 3 decimal places. A circular arc of length 8 ft subtends a central angle of 25. Find the radius of the circle. Round your answer to 3 decimal places. Find the radius of each circle if the area of the sector is 23. (Round your answer to two decimal places.) How many revolutions will a car wheel of diameter 28 inches make as the car travels a distance of seven miles? (Round your answer to the nearest whole number.) Find the side labeled x. Assume a = 9. Find the side labeled x. Round your answer to 5 decimal places. Assume a = 21, θ = 55.

2 Use the figure and the value given below to answer the following questions. Assume A = 2. (a) Express x in terms of trigonometric ratios of θ. (b) Express y in terms of trigonometric ratios of θ. Solve the right triangle. Assume h = 408. (a) Find the length of the shorter side. (Round your answer to two decimal places.) (b) Find the length of the longer side. (Round your answer to two decimal places.) Find x correct to one decimal place. Assume A = 81. From the top of a 160 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? Round your answer to the nearest foot. A 16-ft ladder is leaning against a building. (a) If the base of the ladder is 7 ft from the base of the building, what is the angle of elevation of the ladder? (Round your answer to one decimal place.) (b) How high does the ladder reach on the building? (Round your answer to the nearest whole number.) An airplane is flying at an elevation of 5150 ft, directly above a straight highway. Two motorists are driving cars on the highway on opposite sides of the plane, and the angle of depression to one car is 35 and to the other is 51. How far apart are the cars? Round your answer to the nearest foot. 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 at a distance D = 585 m away measures the angle of elevation to the spot of light to be 45. Find the height h of the cloud cover, correct to the nearest meter. Find the reference angle for the given angle.

3 (a) 120 (b) -210 (c) 765 Find the reference angle for the given angle. (a) (b) (c) (a) 2.4π (b) 2.4 (c) -18π Find the quadrant in which θ lies from the given information. sin(θ) > 0 and cos(θ) < 0 Write the first trigonometric function in terms of the second for θ in the given quadrant. csc θ, cot θ; θ in quadrant III Find the values of the trigonometric functions of θ from the information given. cos(θ) = -9/16, and θ in quadrant III cot θ = 1/15, sin θ < 0 Find the area of a triangle that has the following dimensions. Round your answer to the tenth place. sides of length 8 and 7, and included angle 83. Find the area of the shaded region in the figure where α = π/3, b = 19. (Round your answer correct to the nearest whole number). Use the Law of Sines to find the indicated angle θ. Assume to one decimal place.) C = 67, b = 56.9, c = (Round your answer Use the Law of Sines to find the indicated side x. Assume A = 102, B = 29, c = 185. (Round your answer to one decimal place.)

4 Solve the triangle using the Law of Sines. Assume b = 7, A = 50, nearest hundredth and the angle to the nearest whole number.) C = 100. (Round the lengths to the Use the following information to sketch the triangle, and then solve the triangle using the Law of Sines. (Round the angle to the nearest whole number and the lengths to the nearest tenth.) A = 22, B = 119, c = 53 Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (Below, enter your answers so that C 1 is smaller than C 2. Round your answers to the nearest degree and to the nearest tenth of length.) a = 26, c = 48, A = 26 For the triangle shown, find the length AD. Assume u = 12, v = 12, x = 40, y = 40. (Round your answer to two decimal places.) A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, 6 mi apart, to be 32 and 48, as shown in the figure. Round your answers to the nearest tenth mile. (a) Find the distance of the plane from point A. (b) Find the elevation of the plane A tree on a hillside casts a shadow c ft down the hill. If the angle of inclination of the hillside is b to the horizontal and the angle of elevation of the sun is a, find the height of the tree. Assume a = 56, b = 26 c = 210 ft. (Round your answer to the nearest whole number.) A water tower 30 m tall is located at the top of a hill. From a distance of D = 110 m down the hill, it is observed that the angle formed between the top and base of the tower is 8. Find the angle of inclination of the hill. Round your answer to the nearest tenth degree.

5 Use the Law of Cosines to determine the indicated side x. θ = 82 Use the Law of Cosines to determine the angle θ: x = Use the Law of Cosines to determine the angle θ. (Round your answer to one decimal place.) a = 12, b = 13, c = 23 Solve triangle ABC. (If there is no such triangle enter NONE for each answer. Round your answers to 1 decimal place.) b = 51, c = 32, A = 60 a = 65, c = 52, C = 59 Find the angle θ. (Use either the Law of Sines or the Law of Cosines, as appropriate.) (Round your answer to one decimal place.) a = 10, b = 7, c = 15 Find the angle θ. (Use either the Law of Sines or the Law of Cosines, as appropriate.) (Round your answer to one decimal place.) a = 14, c = 8, C = 30

6 Find the area of the triangle whose sides have the given lengths. (Round your answer to two decimal places.) a = 1, b = 2, c = 2 Find the area of the shaded figure. (Round your answer to two decimal places.) a = 3, b = 5, y = 60 Airport B is 300 mi from airport A at a bearing N 50 E (see the figure). A pilot wishing to fly from A to B mistakenly flies due east at 250 mi/h for 30 minutes, when he notices his error. (a) How far is the pilot from his destination at the time he notices the error? Round your answer to the nearest mile. (b) What bearing should he head his plane in order to arrive at airport B? Round your answer to the nearest degree. A 145 ft tower is located on the side of a mountain that is inclined 32 to the horizontal. A guy wire is to be attached to the top of the tower and anchored at a point 55 ft downhill from the base of the tower. Find the shortest length of wire needed.