Joseph is building a staircase inside a customer’s house. The angle of elevation must be between 30° and 50° for the staircase to pass inspection. He plans to build a base that is 18 feet wide, and the height will be a total of 11 feet. In 1–2 sentences, explain how Joseph can determine the angle of elevation with his dimensions while using inverse trigonometric functions. What is the approximate angle of elevation of the staircase, and will it pass inspection?(2 points)
Joseph can use the inverse trigonometric function tangent to find the angle of elevation, which is equal to arctan(height/base). Using the given dimensions, the approximate angle of elevation of the staircase is arctan(11/18) ≈ 30.96°. Since the angle is within the range of 30° to 50°, the staircase will pass inspection.
