4 Triangle Tactics Copyright © 2026 Pearson Education, Inc. Triangle Tactics (50 – 60 minutes) Learning Objective(s): Students will apply the Pythagorean Theorem to find missing side lengths in right triangles. Students will use sine, cosine, and tangent ratios to solve for unknown sides or angles. Students will recognize and use relationships in 30°– 60°– 90° and 45°– 45°– 90° triangles. Material needed: Student pages: Triangle Tactics Calculator Graph paper (optional) Online graphing tools (optional) Lesson Procedure: Warm–Up 10 minutes Prompt: To build a ramp that must be safe and meet regulations, how could you use math to determine how long the ramp should be, if you know how high it needs to go and the angle it should form? What math tools would help you solve this problem? Discuss: right triangles, Pythagorean Theorem, sine, cosine, tangent, angle of elevation, vertical rise Guided Instruction 10 minutes Present: scenario for Triangle Tactics. Example: A temporary ramp has a vertical rise of 2 feet and a horizontal length of 8 feet. Use the Pythagorean Theorem to find the ramp’s length. √68≈8.25 feet Use the tangent ratio to find the angle of elevation of the ramp. tan–1 (0.25) ≈ 14.04° Review: key terms – angle of elevation, hypotenuse, tangent angle of elevation: the angle formed between the horizontal line of sight and the line of sight to an object that is above the horizontal hypotenuse: longest side of a right triangle, opposite the right angle tangent: trigonometric ratio used in right triangles to compare the opposite side to the adjacent side of a given angle Independent Practice 25 minutes Distribute: student activity Triangle Tactics Allow students to work individually or in pairs. Closure 10–15 minutes Review Answers: 1. Check student sketches; 10 ft 2. a. 13 ft; b. 67.38° 3. 9.9 ft 4. a. 3.88 ft; b. 14.49 ft 5. 3.42 ft 6. 4.76° 7. a. No, the ramp will only reach about 2.12 feet, which is not high enough to meet the 3-foot door height. b. about 17.01 ft long Discuss: How can the Pythagorean Theorem and trigonometric ratios ensure that ramps meet safety standards? Can you think of other everyday applications for which these math tools are important?
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