LATE AND ABSENT HOMEWORK IS ACCEPTED UP TO THE TIME OF THE CHAPTER TEST ON

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1 Trig/Math Anal Name No LATE AND ABSENT HOMEWORK IS ACCEPTED UP TO THE TIME OF THE CHAPTER TEST ON HW NO. SECTIONS ASSIGNMENT DUE TT 1 1 Practice Set D TT 1 6 TT 1 7 TT TT 1 8 & Application Problems 1 9 Application Problems TT 6 1 TT 7 Review Practice Set E Practice Set F Practice Set G Practice Set A #1 Practice Set H Practice Set J Practice Set K # Practice Set L # 9 Practice Set M # 9 1 Practice Set B Practice Set K #1 Practice Set L #8 Practice Set M #1 Practice Set N Practice Set P # Practice Set A # Practice Set C Practice Set P # Practice Set M #10 Practice Set A Solve the triangle given: 1. a 6 b 9. c 1. m A m B 8 c 1. m A a b 6 (Two triangles). Find the area and perimeter of a 1 gon inscribed in a circle with radius1. Practice Set B: Application Problems 1. Find the area of a regular octagon inscribed in a circle of radius 0 cm.. Adjacent sides of a parallelogram have lengths 6 cm and 7 cm and the measure of the included angle is 0. Find the area of the parallelogram.. A ship passes by buoy B which is known to be 000 yards from peninsula P. The ship is steaming east along line BE and PBE is measured as 8. After 10 minutes the ship is at S and PSE is measured as 6. a. How far from the peninsula is the ship when it is at S? b. If the ship continues east what is the closest it will get to the peninsula? (Hint: the closest distance is the perpendicular.) c. How fast (in yd/min) is the ship traveling? d. Ship speeds are often given in knots where 1 knot 1 nautical mile per hour 6080 feet per hour. Convert your answer in part (c) to knots. TMA Assignment List 1 - Triangle Trig Page 1

2 . From points P and Q 180 m apart a tree at T is sighted on the opposite side of a deep ravine. From point P a compass indicates that the angle between the northsouth line and line of sight PT is 7 and that the angle between the north south line and PQ is 78. From point Q the angle between the north south line and QT is. a. How far from P is the tree? b. How far from P is the point on PQ that is closest to the tree?. An isosceles trapezoid has a height of cm and bases cm and 7 cm long. How long are its diagonals? 6. Two airplanes at points A and B in the diagram have elevations of 000 ft and ft respectively. Both are flying east toward an airport control tower at T. From T the angle of elevation of the airplane at A is and the angle of elevation of the airplane at B is.. How far apart (in miles) are the airplanes? (80 ft 1 mi). 7. An airplane at A is flying at a height of 6 mi above Earth s surface at S as shown. a. Find the distance to the nearest tenth of a mile from A to the horizon H (The radius of Earth is about 000 miles.) b. Find the curved distance to the nearest tenth of a mile from S along Earth s surface to H. Practice Set C: Review 1. In ΔABC m A 70 m C 0 c. Find. Find the measure of the smallest angle and the length of side a the area of a triangle with sides 6 and 7.. In Δ ABC b 10 c m A find the. Find the area of a triangle with sides 10 6 length of side a and 1. Adjacent sides of a parallelogram have 6. What is the angle of elevation of the sun lengths 6 cm and 8 cm and the measure of the when a flagpole 7. m high casts a shadow included angle is. Find the area of the m long? parallelogram. 7. A kite 6 m long is a quadrilateral having two sides each m long and two sides each. m long. How wide is the kite? (That is what is the length of the shorter diagonal?) Practice Set D: Solving Right Triangles (Page ) Give lengths to three significant digits and angle measures to the nearest tenth of a degree or nearest ten minutes. Solve each right triangle ABC. 8. Two planes leave an airport at the same time one flying due south at 00 mph and the other flying due northwest at 0 mph. How far apart are they three hours later? 1. A 8.6 c 1. B.8 c 16.. B 71. a 1.8. A 7. b TMA Assignment List 1 - Triangle Trig Page

3 7. a 60 c The height of an isosceles triangle is 10 units and its base is 16 units long. Find its angles. 18. The height of an isosceles trapezoid is 1 units and its bases have lengths and 1 units. Find its angles. 19a. Find the perimeter of a regular pentagon inscribe in a unit circle (a circle with radius 1). 19b. Find the perimeter of a regular pentagon circumscribed about a unit circle. 0a. Repeat exercise 19a for a regular polygon having 10 sides. 0b. Repeat exercise 19b for a regular polygon having 10 sides. Practice Set E: Solving Right Triangles Problems (Page ) Give lengths to three significant digits and angle measures to the nearest tenth of a degree. 1. What is the angle of elevation of the sun. In one minute a plane descending at a when a flagpole. m high casts a shadow constant angle of depression of 11. travels. m long? 100 m along its line of flight. How much altitude has it lost?. A television camera on a blimp is focused on 7. Opposite corners of a small rectangular park a football field with angle of depression 18.. are joined by diagonal paths each 0 m long. A range finder on the blimp determines that Find the dimensions of the park if the paths the field is 180 m away. How high is the intersect at a 6 angle. blimp? 9. From a point 100 m from a building the angles of elevation of the top and bottom of a flagpole atop the building are 6. and 9.. How tall is the flagpole? 1. Two observers 1600 m apart on a straight road measure the angles of elevation of a helicopter hovering over the road between them. If these angles are.0 and 0. how high is the helicopter? 11. Two boats are in line with a tower whose top is 8 m above the water. How far apart are the boats if their angles of depression from the top of the tower are. and 7.? Practice Set F: Law of Cosines (Page 8) Find lengths to three significant digits and angles to the nearest tenth of a degree. Find the indicated part of Δ ABC 1. a b 7 C 0 c. c 11 a 1 B 81 b TMA Assignment List 1 - Triangle Trig Page

4 . c 0 b 0 A 10 a 7. a 7 b 9 c 1 B 9. a 1 b 10 c 18 largest angle 11. a 0.6 b 0.8 c 1. smallest angle 1. Find the lengths of the sides of a parallelogram whose diagonals intersect at a angle and have lengths 6 and 10. (Recall that the diagonals of a parallelogram bisect each other). Practice Set G: Law of Cosines Problems (Page 9) Find lengths to three significant digits and angles to the nearest tenth of a degree. 1. Two planes leave an airport at the same. A cruise ship and a freighter leave port at time one flying due east at 600 km/h and the the same time and travel straight line courses other flying due northwest at 00 km/h. How at 0 km/h and 10 km/h respectively. Two far apart are they two hours later? (hint: To hours later they are 0 km apart. What is the work with smaller numbers use 100 km as the angle between their courses? length unit.). A baseball diamond is a square 90 feet on a side and the pitcher s mound is 60. feet from home plate. How far is it from the mound to first base? 7. A vertical pole 0 m tall standing on a 1 slope is to be braced by two cables extending from the top of the pole to the points on the ground 0 m up the slope and 0 m down the slope. How long must the cables be? Practice Set H: Law of Sines (Page ) Find the indicated part of ΔABC to three significant digits or to the nearest tenth of a degree. If there are two solutions give both of them. 1. a 16 A B 6 b. b.10 A 110 C 0 a. c 0 A C 98 b 7. a 0 b 1 A 0 B 9. a.0 c. C 1 B Practice Set J: Law of Sines Problems (Page ) Give answers to three significant digits. 1. Two angles of a triangle are and 60. How long is the base of an isosceles triangle and the longest side is m. Find the length of if each leg is cm long and each base angle the shortest side. measures18?. A parcel of land is in the shape of an 8. A pilot approaching a foot runway isosceles triangle. The base fronts on a road finds that the angles of depression of the ends and has a length of 61 ft. If the legs meet at of the runway are 1 and1. How far is the an angle of 9 how long are they? plane from the nearer end of the runway? Practice Set K: Solving General Triangles (Page 8) Give lengths to three significant digits and angle measures to the nearest tenth of a degree. Solve the triangles. If there are two solutions find both. If there are no solutions so state. Find the area of each triangle for questions # a 1 B 0 C 0. a b 7 c 9. b 1 c 1 A a 0 b 0 A a 1 b 7 B (Two triangles) 16. Find the lengths of the diagonals of the 1. b 1 c 1 C 0 b1 (Two quadrilateral shown. triangles) TMA Assignment List 1 - Triangle Trig Page

5 Practice Set L: Solving General Triangles Problems (Page 9 60) Given lengths to three significant digits and angle measures to the nearest tenth of a degree.. A television antenna standing on level ground is supported by two cables extending from the top of the antenna to the ground on opposite sides of the antenna. One cable is 00 m long and makes an angle of 8 with the ground. The other cable is 70 m long. Find the acute angle that the second cable makes with the ground and the distance between the cables at the ground. 8. A kite. m long is a quadrilateral having two sides each 1 m long and two sides each m long. How wide is the kite? (That is what is the length of the shorter diagonal?) 9. From the top of a tower 80 m above sea level an observer sights a sailboat at an angle of depression of 9. Turning in a different direction he sights another sailboat at an angle of depression of 1. The angle between these lines of sight is 6. How far apart are the boats? Practice Set M: Areas of Triangles (Page 6) Find the areas of the triangles described. Give answers to three significant digits. 1. A 0 B b 0. b c 18 A. a b 1 c Find the area of a parallelogram that has a 6 angle and sides with lengths 8 and Find the area of a rhombus that has perimeter 60 and an angle of 0 1. Find the area of a regular pentagon whose sides are 10 cm long. Practice Set N: Trig Functions of General Angles (Page 1) Give the reference angle α for each angle θ θ θ θ θ θ θ θ θ 00 State the values of the six trigonometric functions of θ. If a value is undefined so state TMA Assignment List 1 - Triangle Trig Page

6 Practice Set P: Trig Functions of General Angles (Page ) Give the exact values of the six trigonometric functions of the given angle. Use radicals when necessary cos θ 0 < θ < sin θ cosθ > 0 1 a. Give the quadrant of angle θ b. Find the five other trigonometric functions of θ. When radicals occur leave your answer in simplest radical form. 1. cos θ 0 < θ < 70 a. Give the quadrant of angle θ b. Find the five other trigonometric functions of θ. When radicals occur leave your answer in simplest radical form. ANSWERS Practice Set A m A.8 m B m C m C a 1.6 b 17. a. Give the quadrant of angle θ b. Find the five other trigonometric functions of θ. When radicals occur leave your answer in simplest radical form.. sin θ tanθ > 0 a. Give the quadrant of angle θ b. Find the five other trigonometric functions of θ. When radicals occur leave your answer in simplest radical form.. m B 7 m C 89 c 7. m B 1 m C c Practice Set B a. 181 yds b. 107 yds c. 19 yds/min d..7 knots a. 16. b miles 7a. 19 mi. 7b. 09 mi. Practice Set C Practice Set D 1. a 69. b 17 m B 61.. a 1.0 b 11.1 m A 7.. b. c.7 m A 18.. a 7 c 661 B. 7. b m A 6.0 m B a b a b. 6. Practice Set E m. 81 m 7. 8 m by 7. m m m or 0 m m Practice Set F m C m B Practice Set G km ft m and 1. Practice Set H TMA Assignment List 1 - Triangle Trig Page 6

7 Practice Set J m cm. 180 ft ft. Practice Set K 1. area. A 100 b 7.6 c area1. A. B 8. C area88.6 B.7 C. a area99. B 0.7 C 19. c A 79. C 6. c 11.1 or A 100. C. c B 6.1 A 67.9 a 1.7 or B A 1.1 a and 1. Practice Set L..7 m m 9. 0 m Practice Set M Practice Set N sin θ cosθ sin θ cosθ sin θ cosθ 1. tan θ cscθ 1. tan θ cscθ 1. tanθ 1csc θ sec θ cotθ sec θ cotθ secθ cotθ 1 Practice Set P 1 1 sin ( 00 ) cos( 00 ) sin ( 10 ) cos( 10 ) 6. tan ( 00 ) csc( 00 ) 7. tan ( 10 ) csc( 10 ) sec( 00 ) cot ( 00 ) sec( 10 ) cot ( 10 ) 8. 1 sin ( 0 ) cos( 0 ) sin( ) cos( ) tan( ) 1 9. tan ( 0 ) csc( 0 ) csc sec cot sec( 0 ) cot ( 0 ) ( ) ( ) ( ) 1 sin ( 00 ) cos( 00 ) 1. tan ( 00 ) csc( 00 ) sec( 00 ) cot ( 00 ) 8a. cos θ 8b. tan θ csc θ sec θ cotθ a. 7 cos θ b. 7 tan θ csc θ 7 sec θ cotθ a. sin θ 1 7b. 1 tan θ csc θ 1 sec θ cotθ a. 1 sin θ 1b. tan θ csc θ sec θ cotθ TMA Assignment List 1 - Triangle Trig Page 7

8 SPIRAL REVIEW (CLASSWORK) Lesson TT Classwork 1 Find the measure of the angles of an isosceles triangle with an altitude of 11 and a base of 1. 1 Find the length of the perimeter of a regular pentagon inscribed in a circle of radius. 1 Find the length of the perimeter of a regular pentagon inscribed in a circle of radius. Lesson TT Classwork 1 6 Find the measure of the smallest angle in Δ ABC if a 0 b 0 c 0 Lesson TT Classwork 1 6 In Δ ABC find c if a b 7 and C Solve ΔABC if m B 118 m C 6 c 1 Lesson TT Classwork 1 Find the measure of the angles of an 1 6 An observer located km from a rocket isosceles triangle with an altitude of 1 and a launch site sees a rocket at an angle of elevation base of 11. of. How high is the rocket at that moment? 1 7 Find the area of ΔABC if 1 8 Solve ΔABC given a c 19 m B81 m B 0 b 16 c (there are triangles). Lesson TT 6 Classwork 1 Opposite corners of a small rectangular 1 6 A news blimp hovers over a stadium at an park are joined by diagonal paths each 180 m altitude of 1 m. The pilot sights an long. Find the dimensions of the park if the elementary school at a 10 angle of depression. paths intersect at a angle. Find the ground distance between the stadium and the school. 1 7 Two angles of a triangle are and Find the area of ΔABC if and the longest side is 0 m. Find the length of a b 0 c 19 the shortest side. 1 9 Find the area of a regular octagon inscribed in a circle of radius 0 cm. TMA Assignment List 1 - Triangle Trig Page 8