How do i find length of AB in the triangleABC angleB equals 95 degrees angleC equals 24 degrees and line AC equals 17cm how do i find the length of AB?

Answer 1

By use of the sine rule:

sin A / BC = sin B / AC = sin C / AB

Angles B and C are known, as is length AC, so:

sin B / AC = sin C / AB

AB = AC x sin C / sin B

AB = 17cm x sin 24 / sin 95 ~= 6.94cm

The ratios for the sine rule can also be given the other way up:

BC / sin A = AC / sin B = AB / sin C

(I learnt the rule the first way.)

Further, if r is the radius of the triangle's circumcircle, then:

sin A / BC = 1/2r

or

BC / sin A = 2r