A triangle has sides with lengths of 2, 8, and 8. What is the radius of the triangles inscribed circle?

1 Answer
Rui D.
Jan 19, 2016

#.882#

Explanation:

Refer to the figure below

I created this figure using MS Excel

Applying the Law of Sines
#2/sin alpha=8/sin beta#

Because it is a triangle
#alpha+beta+beta=180^@# => #alpha=180^@-2beta#

Then
#1/sin (180^@-2beta)=4/sin beta#

Sines of supplementary angles are equal or #sin (180^@-theta)=sin theta#.
So
#1/(sin 2beta)=4/sin beta#
#1/(2cancel(sin beta)*cos beta)=4/cancel(sin beta)#
#cos beta=1/8# => #beta=82.819^@#

As we can see from the figure
#tan (beta/2)=r/1# => #r=tan(beta/2)#

In case,
#r=tan(82.819^@/2)=.882#

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