A circular park of radius m 10m is situated in a colony. Three girls Ankita,
Shireen and Deepti are sitting at equal distance on its boundary each having
a toy telephone in his hands to talk each other. Find the length of the string
of each phone
Answers
Given : A circular park of radius 10m is situated in a colony
Three girls Ankita, Shireen and Deepti are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other.
To Find : the length of the string of each phone
Solution:
sitting at equal distance
=> Equilateral Triangle
Let say ABC is triangle
and O is center
then AO = BO = CO = Radius = 10 m
as Triangle is equilateral
Hence ∠AOB = ∠BOC = ∠COA = 360°/3 = 120°
AB² = AO² + BO² - 2AO. BO Cos∠AOB
=> AB² = 10² + 10² - 2* 10 * 10 Cos120
=> AB² = 200 - 200(-0.5)
=> AB² = 200 + 100
=> AB² = 300
=> AB = 10√3
length of the string of each phone = 10√3 m
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