a telephone pole is supported by two cables attached to points on the pole 15 ft above ground and to points on the level ground 8 ft from the foot of the pole. what is the total length of the two cables
the cables form the hypotenuse of right-angled triangles
for each one:
h^2 = 15^2 + 8^2 = 289
h = 17
length of 2 such cables = 34 ft
To find the total length of the two cables supporting the telephone pole, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the two cables form two right triangles. Let's label the sides of one of the right triangles as follows:
- The vertical side: 15 ft (height of the pole above ground)
- The horizontal side: 8 ft (distance from the foot of the pole to the point where the cable is attached)
To find the length of the first cable, we'll use the Pythagorean theorem:
Cable 1 = sqrt(15^2 + 8^2)
Simplifying the equation, we have:
Cable 1 = sqrt(225 + 64)
Cable 1 = sqrt(289)
Cable 1 = 17 ft
So, the length of the first cable is 17 ft.
Now, let's label the sides of the second right triangle as follows:
- The vertical side: 15 ft (height of the pole above ground)
- The horizontal side: 8 ft (distance from the foot of the pole to the point where the second cable is attached)
Using the Pythagorean theorem again, we can find the length of the second cable:
Cable 2 = sqrt(15^2 + 8^2)
Simplifying the equation, we have:
Cable 2 = sqrt(225 + 64)
Cable 2 = sqrt(289)
Cable 2 = 17 ft
So, the length of the second cable is also 17 ft.
To find the total length of the two cables, we simply add the lengths:
Total length = Cable 1 + Cable 2
Total length = 17 ft + 17 ft
Total length = 34 ft
Therefore, the total length of the two cables supporting the telephone pole is 34 ft.