maths~~~~~~

在△ABC ,

BC / sinㄥBAC = AC / sinㄥABC

5 / sin(180-80-30-35)° = AC / sin(80+30)°

AC = 8.19152 cm

在△BCD ,

BC / sinㄥBDC = CD / sinㄥDBC

5 / sin(180-30-60-35)° = CD / sin30°

CD = 3.05194 cm

在△ACD ,

AD^2 = AC^2 + CD^2 - 2 AC CD cosㄥACD

AD^2 = 8.19152^2 + 3.05194^2 - 2(8.19152)(3.05194)cos60°

AD^2 = 51.41531

AD = 7.17cm(2位小數)

∠BDC=180-60-35-30
=55°
By sine formula.
sin95°/DB=sin55°/5
DB=5sin95°/sin55°
∠BAC=180°-35°-80°-30°
=35°
By sine formula,
sin35°/AB=sin35°/5
AB=5cm
By cosine formula.
AD^2=AB^2+BD^2-2(AB)(BD)cos80°
AD=7.17cm(cor. to 2 d.p.)