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Geometry UNIT : Triangles Topic: Right Triangle Trigonometry Lesson: Tic-Tac-Toe Trigonometry Content Objective To use trigonometric ratios in problem situations. Language Objective TEKS Vocabulary G.11(C ) develop, apply, and justify triangle similarity relationships, such as right triangle ratios, trigonometric ratios, and Pythagorean triples using a variety of methods Sine, cosine, tangent ratios Opposite Adjacent Hypotenuse Prior Knowledge Students need to know how to set up trigonometric ratios in order to solve for a missing length. Materials Set of problems copied on cardstock Tic-Tac-Toe Board Recording Sheet Teacher Notes: Each pair or group of students will get a set of the word problems. Some problems are more complex than others. Students should draw a picture of each problem they are solving, label it, and then solve and answer the question. Some of the questions require the students to explain in the form of a written response. You may decide to have the students complete on tic-tac-toe in class, and another tic-tactoe for further practice. Ramp It Up In order for ramps to be accessible for individuals with disabilities, there are requirements placed on the design of the ramps. One requirement is that the slope of the ramp cannot rise more than 1 inch for each foot. Therefore, the slope of the ramp cannot be greater than 1 . 12 Brooke is designing a ramp to install at her business. In her design, the ramp makes a 5° angle with the ground and is 24 feet long. Will her ramp meet the requirements for individuals with disabilities outlined above? Justify your answer with a drawing and written explanation. Airplane Landing Commercial airliners fly at an altitude of about 10 kilometers. They start descending toward the airport when they are far away, so that they will not have to dive at a steep angle. If the pilot wants the plane’s path to make an angle of 3 degrees with the ground, what is the distance the plane will travel on this descending path? Submarine Problem A submarine at the surface of the ocean makes an emergency dive, its path making an angle of 21 degrees with the surface. If it goes for 300 meters along its downward path, how deep will it be? How tall is it? A boy, who is 5’6’’ tall, stands on a sidewalk, looks up at a tall house, and wonders how tall it is. Using a meter stick and a clinometers (instrument used to measure the angle of elevation or depression), he determines the measurements shown. About how tall is the building? The Ascending Airplane The climb angle (angle of elevation) of an airplane taking off is 20º. If the airplane maintains that angle until it reaches cruising altitude, what is the approximate horizontal ground distance from that airplane to the point of takeoff when the airplane has reached its cruising altitude of 30,000 feet? (Remember that 1 mile = 5,280 feet.) The Lookout Tower Park rangers use lookout towers to watch for forest fires at great distances. A ranger at the top of a 200-foot tower spots a fire and measures the angle of depression as 2º. How far away is the fire? The Ferris Wheel A Ferris wheel at a local park has eight chairs, and the radius of the wheel is 12 feet. It is shown in the nearby diagram. What is the approximate height of the blue chair above the platform? The Lighthouse A lighthouse that is 50 meters above sea level marks the entrance to a bay. The lighthouse is used to orient ships as well as to provide a lookout point for the local coast guard. A pair of ocean kayakers estimate their distance to the entrance of the bay using the lighthouse. They measure the angle of elevation from their position to the top of the lighthouse to be about 16°. Draw a diagram showing the kayaks in relation to the lighthouse illustrating the angle of elevation. Knowing the height of the lighthouse and the angle of elevation from the kayakers to the top of the lighthouse, calculate the kayakers’ distance to the entrance of the bay. Statue of Liberty Linda gets a nose-bleed whenever she is 300 feet above ground. During a class fieldtrip, her teacher asked if she wanted to climb to the top of the Statue of Liberty. Since she does not want to get a nose-bleed, she decided to take some measurements to figure out how high the torch of the statue is . She found a spot directly under the torch and then measured 42 feet away and determined that the angle up to the torch was 82°. Her eyes are 5 feet above the ground. Should she climb to the top or will she get a nose-bleed? Draw a diagram that fits this situation. Justify your conclusion. Tic-Tac-Toe Trigonometry The Ferris Wheel The Lighthouse The Descending Submarine Airplane Landing Statue of Liberty The Look Out Tower The Ascending Airplane The Tall House Ramp it Up Tic-Tac-Toe Recording Sheet Write the name of the problem. Draw a picture and label it. Solve the problem.