Question

A triangle has sides A, B, and C. The angle between sides A and B is `(pi)/4`. If side C has a length of `6` and the angle between sides B and C is `( 3 pi)/8`, what are the lengths of sides A and B?

Answer 1

Length of sides `A and B` are `7.84 ,7.84` unit respectively.

Explanation:

Angle between Sides `A and B` is `/_c= pi/4=180/4=45^0`

Angle between Sides `B and C` is `/_a= (3pi)/8=67.5^0 :.`

Angle between Sides `C and A` is

`/_b= 180-(45+67.5)=67.5^0 ; C=6`

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=6 :. B/sinb=C/sinc` or

`B/sin67.5=6/sin45 or B= 6* (sin67.5/sin45) ~~ 7.84 (2dp)`

Similarly `A/sina=C/sinc:. A/sin67.5=6/sin 45` or

`A= 6* (sin 67.5/sin45) ~~ 7.84 (2dp)`

Length of sides `A and B` are `7.84 ,7.84` unit respectively.[Ans]