To find the angle of elevation from the base of the stairs to the bottom of the door, we can use the inverse tangent function.
First, we need to calculate the height of each step. Since the total height is 3 feet and there are 3 steps, each step will be 1 foot high.
Next, we need to calculate the length of the hypotenuse of the right triangle formed by the height of each step and the distance from the wall (5 feet). Using the Pythagorean theorem, we have:
hypotenuse^2 = 1^2 + 5^2
hypotenuse^2 = 1 + 25
hypotenuse^2 = 26
hypotenuse = sqrt(26) = 5.1 feet
Finally, we can calculate the angle of elevation using the inverse tangent function:
angle = arctan(1/5) = arctan(0.2) ≈ 11 degrees
Therefore, the angle of elevation from the base of the stairs to the bottom of the door is approximately 11 degrees.
Stairs are built using horizontal planks placed within a right triangle dimension. If the ratio of the base and height of the triangle portion are not measured properly, the staircase may be too steep. Imagine you are building a short staircase for your garage that consists of three steps. The height from the garage floor to the bottom of the door is three feet, and you plan to build the stairs five feet out from the wall. Using the inverse of tangent, what is the angle of elevation from the base of the stairs to the bottom of the door? Round your answer to the nearest whole degree.
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