Question

Find the length arc of DB. Leave your answer in terms of pi.

Answer 1

Length of arc DB = 14 π feet

Solution:

Radius AB = 18 feet

DC is the diameter of the circle.

∠CAB = 40°

Sum of the adjacent angles in a straight line = 180°

m∠DAB + m∠CAB = 180°

m∠DAB + 40° = 180°

Subtract 40° from both sides.

m∠DAB = 140°

To find the length of arc DB:

$\text{Arc length} =2 \pi r\left(\frac{\theta}{360}\right)$

$=2 \pi \times 18\left(\frac{140^\circ}{360}\right)$

$=2 \pi \left(\frac{140^\circ}{20}\right)$

= $14\pi$ feet

Length of arc DB = 14 π feet