Question

A triangle has sides A, B, and C. The angle between sides A and B is `(pi)/3`. If side C has a length of `1` and the angle between sides B and C is `( pi)/8`, what are the lengths of sides A and B?

Answer 1

Length of sides `A and B` are `0.44 and 1.14` unit respectively.

Explanation:

Angle between Sides `A and B` is `/_c= pi/3=180/3=60^0`

Angle between Sides `B and C` is `/_a= pi/8=180/8=22.5^0 :.`

Angle between Sides `C and A` is

`/_b= 180-(60+22.5)=97.5^0`

The sine rule states if `A, B and C` are the lengths of the sides

and opposite angles are `a, b and c` in a triangle, then:

`A/sina = B/sinb=C/sinc ; C=1 :. B/sinb=C/sinc` or

`B/sin97.5=1/sin60 or B= 1* (sin97.5/sin60) ~~ 1.14 (2dp)`

Similarly `A/sina=C/sinc` or

`A/sin22.5=1/sin60 or A= 1* (sin22.5/sin60) ~~ 0.44 (2dp)`

The length of sides `A and B` are `0.44 and 1.14` unit

respectively. [Ans]