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almond37 [142]
3 years ago
9

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

Mathematics
1 answer:
lyudmila [28]3 years ago
6 0

Length of arc DB = 14 π feet

Solution:

Radius AB = 18 feet

DC is the diameter of the circle.

∠CAB = 40°

<em>Sum of the adjacent angles in a straight line = 180°</em>

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

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