In a parking garage, there are 20 feet between each level. Each ramp to a level is 130 feet long. Find the measure of the angle of elevation.
To find the measure of the angle of elevation, we can use trigonometry. The angle of elevation is the angle between the ground and the line of sight from the ground to the top of the ramp.
Let's assume that the height of each level of the parking garage is h feet.
The opposite side of the triangle is the height of the level, h.
The adjacent side is the distance between the ramp and the level, 20 feet.
The hypotenuse is the length of the ramp, 130 feet.
Using the tangent function, we can write:
tan(angle) = opposite/adjacent
tan(angle) = h/20
To find the angle, we need to take the inverse tangent (arctan) of both sides:
angle = arctan(h/20)
Therefore, the measure of the angle of elevation is arctan(h/20).
To find the measure of the angle of elevation, we need to use basic trigonometry.
Here's how you can solve the problem step by step:
Step 1: Draw a diagram to visualize the situation. Sketch a right triangle that represents the parking garage. Label one side as the horizontal distance (130 feet) and another side as the vertical height (20 feet).
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| \
| \
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| \ 20 feet
| \
| \
| \
__________|_____________\________
130 feet
Step 2: Identify the trigonometric function that relates the angle of elevation to the given sides. In this case, since we have the opposite side (vertical height) and the adjacent side (horizontal distance), we should use the tangent function.
Step 3: Apply the tangent function to solve for the angle of elevation. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, we have:
tan(angle) = opposite/adjacent
tan(angle) = 20/130
Step 4: Use a calculator to find the inverse tangent (tan^(-1)) of the above ratio to determine the angle's measure:
angle = tan^(-1)(20/130)
Step 5: Calculate the angle using a calculator:
angle ≈ 8.938° (rounded to three decimal places)
Therefore, the measure of the angle of elevation is approximately 8.938 degrees.
Remember to always double-check your calculations and units to ensure accuracy.