Question

The red stripe on a barber pole makes two complete revolutions around the pole. The pole is 260 cm high, and 14 cm in diameter. How long is the stripe? What angle does it make with the horizon?

Answer 1

Answer:

$\boxed{\text{274.5 cm; }71.3^{\circ}}$

Step-by-step explanation:

If we open the surface of the pole and lay it flat, we will get a rectangle with the red stripe as a diagonal.

l = 260 cm.

The width of the rectangle is enough for two revolutions (i.e., twice the circumference).

w = 2C = 2 × 2πr = 4π × 14/2 = 28π cm = 87.96 cm

Length of stripe

The stripe is the diagonal of the rectangle.

d² = 260² + (28π)² = 67 600 + 87.96² = 67 600 + 7738 = 75 338

d = √(75 338) = 274.5 cm

Angle with horizontal

tanθ = 260/(28π) = 260/87.96 =2.956

θ = arctan2.956

θ = 71.3°

The stripe is $\boxed{ \text{274.5 cm}}$ long and the angle with the horizontal is $\boxed{71.3^{\circ}}$.