Jenny is standing 400 feet from an 800 foot tall building. Jenny walks away from the building to a point where the angle of elevation to the top of the building is 22°. What is the angle of elevation to the top of the building from Jenny’s original position, and how far away from the building did she move?
At 22°, her distance x from the building can be found by
800/x = tan 22°
Her original angle of elevation θ comes from
tanθ = 800/400
To find the angle of elevation to the top of the building from Jenny's original position, we can use trigonometry. Let's call the angle of elevation from Jenny's original position "x".
We have a right triangle formed by Jenny, the building, and the point where she moved. The height of the building is the opposite side of the angle of elevation, and the distance from Jenny to the building is the adjacent side. Using the tangent function, we can set up the following equation:
tan(x) = (opposite side) / (adjacent side)
tan(x) = 800 / 400
Now, let's solve for x by taking the inverse tangent (arctan) of both sides:
x = arctan(800 / 400)
Using a calculator, we find that x is approximately 63.43°.
Now, let's find out how far away from the building Jenny moved. We'll call this distance "d". To do this, we can use trigonometry again, this time using the angle of elevation of 22°.
We can set up another right triangle, where the height of the building is the opposite side and "d" is the adjacent side. Using the tangent function, we have:
tan(22°) = (opposite side) / (d)
tan(22°) = 800 / (d)
Now, let's solve for d by rearranging the equation:
d = 800 / tan(22°)
Using a calculator, we find that d is approximately 2036.73 feet.
Therefore, the angle of elevation to the top of the building from Jenny's original position is approximately 63.43°, and she moved approximately 2036.73 feet away from the building.