Asked by Dancan
A chord AB of length 13cm subtends an angle of 67° at the circumferance ofa circle centr O.Find the radius
Answers
Answered by
Dancan
I need soln of it
Answered by
mathhelper
Did you make your sketch?
If so, you should be able to see that we could just use the
cosine law:
13^2 = r^2 + r^2 - 2(r)(r)cos 67°
169 = 2r^2 - 2r^2(.39073..)
169 = 2r^2( 1 - .39073..)
r^2 = 169/(2(.60926..)
r^2 = 138.69...
r = appr 11.777 cm
or
half the central angle would be 33.5°
looking at one of the right-angled triangles after sketching
the height ....
sin 33.5 = 6.5/r
r = 6.5/sin33.5 = 11.777, just as before
If so, you should be able to see that we could just use the
cosine law:
13^2 = r^2 + r^2 - 2(r)(r)cos 67°
169 = 2r^2 - 2r^2(.39073..)
169 = 2r^2( 1 - .39073..)
r^2 = 169/(2(.60926..)
r^2 = 138.69...
r = appr 11.777 cm
or
half the central angle would be 33.5°
looking at one of the right-angled triangles after sketching
the height ....
sin 33.5 = 6.5/r
r = 6.5/sin33.5 = 11.777, just as before
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