Question

how to calculate the exact radius if the side of inscribe triangle is 7 cm, 7 cm, 7 cm ?? please....help me

Answer 1

So if it is a inscribed triangle, we have a circle touching all points of the triangle



than we know that it is an equalateral triangle so it was 60-60-60 degree angles.

now create the height of the triangle, by making a line from a point to the base



we now have a 30-60-90 triangle with hyp of 7

so all we need know is L=s√3
H=2s
H=7 then 7=2s and s=7/2

then L=(7/2)√3

but were not done yet because we need the bottom part of the lenght

if you make another triangle underneath, youll get another 30-60-90

and all you need to do is see than 7/2=L for this trinagle when it was S for the 1st one

L=s√3
7/2(√3)=s
(7/6)√3=s

(7√3)/2 + (7√3)/6= (28√3)/6=(14√3)/3=r