From Base to Branch 1 Copyright © 2026 Pearson Education, Inc. From Base to Branch An outdoor adventure company is designing zipline courses and climbing walls for a nature park. Each structure must meet safety guidelines. This requires precise calculations of angle measures and side lengths using right triangles. The team must use trigonometric ratios and the Pythagorean Theorem to ensure accurate and safe construction when measuring the heights of platforms from a fixed base or finding the length of the cable needed to support a diagonal climb. Special right triangles, including 30°– 60°– 90° and 45°– 45°– 90°, also help the team complete calculations more efficiently when working with common setups. 1. A ladder is leaning against a wall. The top of the ladder is 15 feet up the wall and its bottom is 9 feet from the wall. How long is the ladder? Round your answer to the nearest hundredth. 2. A ramp rises 4 feet over a 10-foot base. What is the angle of elevation? Round your answer to the nearest hundredth. 3. A rope bridge with one side forming a 40° angle with the ground connects to a platform that is 12 feet above the ground. a. Use the sine ratio to find the side length. Round your answer to the nearest hundredth. b. What would happen to the length of the side if the platform height were increased? Write a brief, precise explanation using appropriate tone and word choices. 4. A triangular window at the base of the course has two equal sides, each 10 inches long, forming a right angle. a. What type of triangle is the window? b. What is the length of the hypotenuse? Round your answer to the nearest hundredth. Justify your answer using both math and descriptive language.
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