Triangle Tactics 1 Copyright © 2026 Pearson Education, Inc. Triangle Tactics A construction crew is building wheelchair-accessible ramps for a community center. Safety codes require ramps to rise at a specific angle and meet certain length and height requirements. Engineers and builders must use right triangle relationships, including trigonometric ratios and the Pythagorean Theorem, to calculate the length of a ramp, the angle of elevation, or the vertical rise, depending on the building’s layout. These calculations are critical not only for meeting regulations, but also for ensuring that the ramp is safe, smooth, and usable for all individuals. 1. The construction crew is planning a small access ramp that rises 6 feet vertically and runs 8 feet horizontally. Make a rough sketch, labeling each side. What is the length of the ramp? 2. A temporary ramp is built leading from the sidewalk to a stage at the center. The vertical rise from the ground to the stage is 12 feet. The base of the ramp is 5 feet from the stage. a. How long is the stage? b. What is the angle of elevation of the ramp from the ground to the stage platform? Round your answer to the nearest hundredth. 3. A ramp section is shaped as a 45°– 45°– 90° triangle with legs equal in length. If the vertical rise is 7 feet, what is the length of the ramp? Round your answer to the nearest tenth. 4. The crew is building a sloped roof above the entryway of the ramp. The roof is supported by a beam 15 feet long placed at a 15° angle. A right triangle is formed by the sloped roof, where the beam acts as the hypotenuse and the angle of elevation is 15°. a. What is the vertical height of the triangle formed by the roof? Round your answer to the nearest hundredth. b. What is the length of the adjacent side of the triangle formed? Round your answer to the nearest hundredth.
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