Mr. Box lives on the fourth floor of a building and looks out of his window 46 feet above the sidewalk. A cat on the sidewalk below hears the window open and looks up at an angle of elevation of 75º. How far is the cat in feet from the edge of the building? (Enter only the number of feet.)
Tan75=46/d
solve for d.
Do I multiply tan75 times 46?
To find the distance between the cat and the edge of the building, we can use trigonometry. Let's denote this distance as "x".
First, we need to find the height of the building above the sidewalk. Since Mr. Box's window is 46 feet above the sidewalk, the height of the building is also 46 feet.
Let's visualize the situation. We have a right triangle formed by the height of the building (46 ft), the distance from the cat to the edge of the building (x ft), and the line of sight from the cat to Mr. Box's window.
The angle of elevation from the cat's perspective is 75 degrees. This means that the angle between the line of sight and the ground is 90 - 75 = 15 degrees.
Now, we can use the tangent function:
tan(15 degrees) = opposite/adjacent
tan(15 degrees) = 46/x
To find x, we can rearrange the equation:
x = 46 / tan(15 degrees)
Using a calculator, we find:
x ≈ 162.2 feet
Therefore, the cat is approximately 162.2 feet from the edge of the building.