Three boys Rohan ,Manoj and Naman are sitting on the boundary of a circular Garden such that the distance between any two of them is 90m find the radius of Garden
Answers
Answer:
The radius of circle = 30√3 m
Step-by-step explanation:
From the figure attached with this answer shows the correct scenario of the question.
The triangle ABC is an equilateral triangle with sides are equal.
O is the center of circle.
OC is the radius of circle.
To find the radius of circle
Consider the triangle OCD. The angles of OCD are 30°, 60°, anf 90°
Therefore the sides are in the ratio 1 : √3 : 2
CD = 45
OD : CD : OC = 1 : √3 : 2
OD = 45/√3 = 15√3
OC = 2 * 15√3 = 30√3
Therefore the radius of circle = 30√3
Answer:
51.96 m
Step-by-step explanation:
Three boys Rohan ,Manoj and Naman are sitting on the boundary of a circular Garden such that the distance between any two of them is 90m find the radius of Garden
They are Sitting at vertex of an equilateral triangle as well
with sides = 90 m
if we Draw lines from these three vertex to center we can form 3 Similar Triangles
with two Sides = Radius
and one Side = 90 m
Three triangles are similar so angle formed at center will be equal
let say it is x
then 3x = 360
=> x = 120°
Angle formed at center = 120°
Remaining Two angles = (180° 120°)/2 = 30° ( as Two Sides are equal to Radius)
Using triangle Identity
Side/Sin(opposite angles) are equal
90/Sin 120° = Radius/Sin 30°
Sin120° = Sin 60°
=> Radius = 90 Sin30°/Sin60°
=> Radius = 90 * (1 / 2) / (√3 /2)
=> Radius = 90/√3 m
=> Radius = 30√3 m
=> Radius = 30 × 1.732
=> Radius = 51.96 m
Radius of Garden = 51.96 m