a guy wire is connected 3 ft. from the top of a pole. The guy wire is 36 ft long and it is fastened to an anchor in the ground that is 12ft. from the base of the pole. How tall is the pole? (nearest tenth)
PLEASE HELP!
=)
this is a right triangle
the base is 12ft
hypotenuse is 36ft
x^2 + 12^2 = 36^2
x^2 = 36^2 - 12^2
x^2 = 1152
x = 33.9ft
the pole is 33.9ft + 3ft = 36.9ft
To find the height of the pole, we'll use the concept of similar triangles. Let's denote the height of the pole as 'h'.
We have a right triangle formed by the pole, the guy wire, and the ground. The guy wire acts as the hypotenuse of this right triangle, with a length of 36 ft. The distance from the anchor to the base of the pole forms one of the legs of the right triangle, and it measures 12 ft.
Now, draw a line connecting the top of the pole and the point where the guy wire is connected. This line represents the other leg of the right triangle. We can call the length of this line 'x', which is the distance from the top of the pole to the point where the guy wire is connected.
Since the guy wire is connected 3 ft from the top of the pole, the remaining distance from the point of connection to the top of the pole is 'h - 3'. Therefore, the total length of the line connecting the top of the pole and the point where the guy wire is connected is 'x + h - 3'.
Now, we can use the concept of similar triangles to set up a proportion:
x/(h - 3) = 12/36
We know that x + h - 3 = 36, as the length of the hypotenuse is 36 ft.
Let's solve this proportion:
36x = 12(h - 3)
36x = 12h - 36
Rearranging the equation:
12h - 36 - 36x = 0
Dividing the equation by 12:
h - 3x = 0
Now, substitute h - 3x = 0 into x + h - 3 = 36:
x + 3x = 36
4x = 36
x = 9
Substitute x = 9 into h - 3x = 0:
h - 3(9) = 0
h - 27 = 0
h = 27
The height of the pole is 27 ft.