SOLUTION: Two circles of radii 4cms and 1cm touch each other externally,and 'x' is the angle contained by their direct common tangents. Then the value of sinx is,,?

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Question 726536: Two circles of radii 4cms and 1cm touch each other externally,and 'x' is the angle contained by their direct common tangents.
Then the value of sinx is,,?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
BC=1 and DE=4 are radii to the points of tangency.
They are perpendicular to tangent AE, so ABC and ADE are similar right triangles.
If AB=y, AD=AB%2B1%2B4=y%2B5.
In triangles ABC and ADE,
sin%28DAE%29=1%2Fy=4%2F%285%2By%29 --> 4y=5%2By --> 3y=5 --> y=5%2F3
So sin%28DAE%29=1%2F%285%2F3%29=3%2F5 ---> cos%28DAE%29=4%2F5
x=2%28DAE%29 so sin%28x%29=sin%282DAE%29=2sin%28DAE%29cos%28DAE%29=2%283%2F5%29%284%2F5%29=24%2F25=0.96