When she is outdoors, Tasha the dog, is tied to a stake in the center of a circular area of radius 24 feet. The angle between her dog bourse and her favorite hydrant is 65 degrees. What is the length of the arc from her dog house to the hydrant, following minor arc DG, to the nearest foot.

The length of the arc from her dog house to the hydrant is 69 ft.

length of arc = ∅ / 360 × 2πr

where

r = radius

π = 3.14159

∅ = subtended angle = 165°

Therefore,

r = 24 ft

length of arc = 165 / 360 × 2 × 3.14159 × 24

length of arc = 24881.3928 / 360

length of arc = 69.11498

length of arc = 69 ft

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the length of the arc from her dog house to the hydrant is 69 feet

Step-by-step explanation:

The formula for determining the length of an arc is expressed as

Length of arc = θ/360 × 2πr

Where

θ represents the central angle.

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

Radius, r = 24 feet

θ = 165 degrees

Therefore,

Length of the minor arc, DG = 165/360 × 2 × 3.14 × 24

Length of arc = 69 feet rounded up to the nearest feet.

both equations and proportions are better.

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°