A 24-foot piece of siding is cut into three pieces so that the second piece is twice as long as the first piece and the third piece is five times as long as the first piece. If x represents the length of the first piece, find the lengths of all three pieces.

first piece = 3 feet

Second piece = 6 feet

Third piece = 15 feet.

Step-by-step explanation:

The total length of the siding is 24 feet.

It is cut into three pieces so that the second piece is twice as long as the first piece. If x represents the length of the first piece, then the length of the second piece is 2x.

If the third piece is five times as long as the first piece, then the length of the third piece would be

5x. Therefore,

x + 2x + 5x = 24

8x = 24

x = 24/8

x = 3 feet

Length of the second piece = 2 × 3 = 6 feet.

Length of the third piece = 5 × 3 =

15 feet.

11.2

step-by-step explanation:

when doing tangent the tangent of the angle is equal to the opposite side from the angle over the adjacent side to the angle.

tan43 = x / 12

move 12 over by multiplying each side by 12

12tan43 = x

x = about 11.2