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091916 Solving Missing Angles.notebook September 19, 2016 Monday, September 19, 2016 Trigonometry, Period 2 Lesson Overview: • Warm Up Exercise • Go over homework • Unit 2: Right Triangle Trigonometry > Solving for Missing Angles 1 091916 Solving Missing Angles.notebook September 19, 2016 Warm Up: 1. From a 125ft observation tower on the coast, an observe sights a boat. The angle of depression of the boat is 6°. How far is the boat from the coast? 2. From the top of a 120 ft high tower, an air traffic controller observes an airplane on the runway at an angle of depression of 19°. How far from the base of the tower is the airplane? 2 091916 Solving Missing Angles.notebook September 19, 2016 3. The angle of elevation from point A to the top of a hill is 49°. If point A is 400 feet from the base of the hill, how high is the hill? 4. The angle of depression from a balloon on a 75ft string to a person on the ground is 36°. How high is the balloon? 5. A 14ft ladder is learning against a house. The angle formed by the ladder and the ground is 72°. a. Determine the distance, d, from the base of the ladder to the house. b. Determine the height, h, the ladder reaches up the side of the house. 3 091916 Solving Missing Angles.notebook September 19, 2016 Questions on the homework? 4 091916 Solving Missing Angles.notebook September 19, 2016 5 091916 Solving Missing Angles.notebook September 19, 2016 6 091916 Solving Missing Angles.notebook September 19, 2016 Solving Missing Angles Using Trig Functions Inverse trigonometric functions have side length ratios as their inputs and angles as their outputs. Therefore, when we solve for missing angles of right triangles, we will ALWAYS utilize our inverse trigonometric functions. Inverse trigonometric functions are NEVER the same as our RECIPROCAL trigonometric functions. 7 091916 Solving Missing Angles.notebook September 19, 2016 Steps for solving for a missing angle of a right triangle: 1. Determine which TRIGONOMETRIC RATIO to use after setting up a DIAGRAM with an accompanying EQUATION. 2. Take the INVERSE of both sides of the equation. 3. Type into the calculator for an answer. (ALWAYS hit the 2ND key FIRST!!) 8 091916 Solving Missing Angles.notebook September 19, 2016 9 091916 Solving Missing Angles.notebook September 19, 2016 10 091916 Solving Missing Angles.notebook September 19, 2016 11 091916 Solving Missing Angles.notebook September 19, 2016 12 091916 Solving Missing Angles.notebook September 19, 2016 1. A plane takes off at an elevation of 20°. In its path is the tower of 170 ft. If the plane at takeoff is 500 feet from the tower, what is the altitude of the plane? Will it clear the height of the tower? If yes, by how much? 2. The angle of depression from the top of a tower to a boulder on the ground is 38°. If the tower is 25m high, how far from the base of the tower is the boulder? 13 091916 Solving Missing Angles.notebook September 19, 2016 3. A hot air balloon hovers 75 feet above the ground. The balloon is tethered to the ground with a rope that is 125 feet long. At what angle of elevation, E, is the rope attached to the ground? Round your answer to the nearest hundredth of a degree. 4. A submersible traveling at a depth of 250 feet dives at an angle of 15° with respect to a line parallel to the water’s surface. It travels a horizontal distance of 1500ft during the dive. What is the depth of the submersible after the dive? 14 091916 Solving Missing Angles.notebook September 19, 2016 Communicator Board Activity You will answer the questions in the following order. For each question, you will answer it independently and then compare your answer with a partner. If your answers match, check against the key that it's correct. If so, find a new partner who is on the same numbered problem as you and repeat the process. 7. 1. 6. 3. 8. 2. 4. 5 15 091916 Solving Missing Angles.notebook September 19, 2016 Answer Key to Communicator Boards Activity 16 091916 Solving Missing Angles.notebook September 19, 2016 17 091916 Solving Missing Angles.notebook September 19, 2016 18 091916 Solving Missing Angles.notebook September 19, 2016 Homework 11: Solving Missing Angles of Right Triangles Unit 2 Celebration of Knowledge (Right Triangle Trigonometry) on Wednesday, September 21st 19
