Find the sides of the triangle

Question

Answer 1

Draw the geometric diagram

From ∆BDC

sinθ =BD/BC

BC =BD/sinθ

    =5/sinθ

Opposite angles are equal

∠ABF =θ

rom triangle ∆ABF

cosθ =BF/AB

AB =BF/cosθ

    =4/cosθ

AC =AB+BC

     = 4/cosθ +5/sin θ