If XY = 78 miles and mXY = 70°, then determine the radius of circle H.
1 answer:
Answer:
r ≈ 187. 70 miles
Step-by-step explanation:
The picture represent the question. XY is an arc and it is 78 miles . mXY = 70° . The length of the arc is known and the center angle is also known .We can use the formula for length of arc to get the radius of the circle.
length of arc = ∅/360 × 2πr
where
∅ = 70°
r = ?
length of the arc = 78 miles
78 = 70/360 × 2πr
78 = 140/360 × 3.14 × r
78 = 43.96/36 × r
78 = 14.96r/36
cross multiply
14.96r = 2808
r = 2808/14.96
r = 187.70053476
r ≈ 187. 70 miles
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