A building was 210 ft high and a guy was 8 ft from the top and let down a wire that is .44 radians (degrees) to the ground... How long is the wire?
cosineTheta=202/Length
theta=.44 rad
solve for length
A = (0.44/6.28) * 360o = 25.2o
sin A = h/L
L = h/sin A = 202/sin25.2 = 474 Ft.
-11 1/8+15 5/12=
To find the length of the wire, we can use trigonometry.
First, let's visualize the situation. We have a building that is 210 ft high, and a guy who is 8 ft from the top of the building. The wire that is being let down by the guy forms an angle of 0.44 radians (or approximately 25.26 degrees) with the ground.
Now, we can use the concept of trigonometry to find the length of the wire. In this case, we can use the tangent function, which relates the opposite side (the height of the building) to the adjacent side (the distance of the guy from the top of the building).
The formula for the tangent function is:
tan(angle) = opposite / adjacent
In this case, we want to find the opposite side, which is the length of the wire. We have the angle (0.44 radians) and the adjacent side (210 ft - 8 ft = 202 ft).
Using the tangent function, we can rearrange the formula to solve for the opposite side:
opposite = tan(angle) * adjacent
Plugging in the values we have:
opposite = tan(0.44 radians) * 202 ft
Now, we can calculate the length of the wire using a calculator or a trigonometry table:
tan(0.44 radians) ≈ 0.4577
So, the length of the wire is:
opposite = 0.4577 * 202 ft = 92.6 ft (rounded to one decimal place)
Therefore, the length of the wire is approximately 92.6 ft.