A square canopy is supported on 4 corners by poles. Each pole is supported by 3 cables, each cable is attached to the top of the 12 foot pole and 5 feet away from the base. Find he total length needed for all of the cables.
12 cables
length of one = L
L^2 = 144 + 25 = 169
L = 13
(just in case you do not know about 5, 12, 13 triangle)
12 * 13
To find the total length needed for all of the cables, we need to calculate the length for each cable and then sum them up.
Let's break it down step by step:
1. The canopy is supported on 4 corners, so there are 4 poles in total.
2. Each pole is supported by 3 cables, so we need to calculate the length for one cable and then multiply it by 3.
3. The length of each cable can be found using the Pythagorean theorem, as we have a right-angled triangle formed by the pole, the base, and the cable. The height of the triangle is the height of the pole (12 feet), and the base is given as 5 feet.
4. To find the length of the cable, we use the formula: length of cable = square root of (height^2 + base^2), where the height is 12 feet and the base is 5 feet.
5. Solving the equation, we get: length of cable = sqrt(12^2 + 5^2) = sqrt(144 + 25) = sqrt(169) = 13 feet.
6. Since each pole has 3 cables, the total length for one pole would be 3 times the length of one cable, which is 3 * 13 = 39 feet.
7. Finally, to find the total length needed for all of the cables, we multiply the total length for one pole by the number of poles: 39 feet * 4 poles = 156 feet.
Therefore, the total length needed for all of the cables is 156 feet.